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CBSE Worksheets for Class 11 Maths

CBSE Worksheets for Class 11 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Maths Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Maths Number of Worksheets: 42

CBSE Class 11 Maths Worksheets PDF

All the CBSE Worksheets for Class 11 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Maths Worksheet. CBSE Worksheets for Class 11 Math can also use like assignments for Class 11 Maths students.

Binomial Theorem

• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 1
• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 2

Complex Numbers and Quadratic Equation

• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 1
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 2
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 3
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 4
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 5
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 6

Conic Sections

• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 1
• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 2

Introduction To 3Dimensional Geometry

• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 1
• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 2

Linear Inequalities

• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 1
• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 2

Permutations and Combinations

• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 1
• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 2

Principle of Mathematical Induction

• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 1
• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 2

Probability

• CBSE Worksheets for Class 11 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 11 Mathematics Probability Assignment 2

Relations and Functions

• CBSE Worksheets for Class 11 Mathematics Relations and Functions Assignment

Sequences and Series

• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 4
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 5
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 6
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 7
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 8
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 1
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 2
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 2

Straight Lines

• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 1
• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 2

Trigonometric Ratios

• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 1
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 2
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 3
• CBSE Worksheets for Class 11 Mathematics Mathematical Reasoning Assignment

Advantages of CBSE Class 11 Maths Worksheets

• By practising NCERT CBSE Class 11 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 11 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 11 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 11 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Math Worksheets to secure good score.

CBSE Worksheets For Class 11

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NCERT Solutions Class 11 Computer Science Chapter 5 Getting Started with Python

NCERT Solutions Class 11 Computer Science Chapter 5 Getting Started with Python: National Council of Educational Research and Training Class 11 Computer Science Chapter 5 Solutions – Getting Started with Python. NCERT Solutions Class 11 Computer Science Chapter 5 PDF Download.

NCERT Solutions Class 11 Computer Science Chapter 5: Overview

Question 1. Which of the following identifier names are invalid and why?

i Serial_no.                     v Total_Marks

ii 1st_Room                   vi total-Marks

iii Hundred$                   vii _Percentage

iv Total Marks                viii True

i) Serial_no. :- Invalid

Reason- (.) is not allowed in identifier

ii) 1st_Room :- Invalid

Reason- identifier can’t start with number

iii) Hundred$ :-  Invalid

Reason- We can’t use special symbol $ in identifier

iv) Total Marks :- Invalid

Reason- We can’t use space between in identifier

v) Total_Marks :- Valid

Reason- We can use underscore between in identifier

vi) total-Marks :- Invalid

Reason- We can’t use hyphen between in identifier

vii) _Percentage:- Invalid

Reason- Identifier can’t begin with underscore

viii) True :- Invalid

Reason- We can’t use keyword as a identifier

Question 2 . Write the corresponding Python assignment statements:

a) Assign 10 to variable length and 20 to variable breadth.

b) Assign the average of values of variables length and breadth to a variable sum.

c) Assign a list containing strings ‘Paper’, ‘Gel Pen’, and ‘Eraser’ to a variable stationery.

d) Assign the strings ‘Mohandas’, ‘Karamchand’, and ‘Gandhi’ to variables first, middle and last.

e) Assign the concatenated value of string variables first, middle and last to variable fullname. Make sure to incorporate blank spaces appropriately between different parts of names.

length = 10

breadth = 20

Sum = (length + breadth)/2

Stationary=[‘Paper’ ,  ‘Gel Pen’ , ‘Eraser’

first = ‘Mohandas’

middle= ‘Karamchand’

last= ‘Gandhi’

fullname = first +” “+ middle +” “+ last

Question 3. Write logical expressions corresponding to the following statements in Python and evaluate the expressions (assuming variables num1, num2, num3, first, middle, last are already having meaningful values):

a) The sum of 20 and –10 is less than 12.

b) num3 is not more than 24.

c) 6.75 is between the values of integers num1 and num2.

d) The string ‘middle’ is larger than the string ‘first’ and smaller than the string ‘last’.

e) List Stationery is empty.

Question 4. Add a pair of parentheses to each expression so that it evaluates to True.

a) 0 == 1 == 2

b) 2 + 3 == 4 + 5 == 7

c) 1 < -1 == 3 > 4

Question 5 . Write the output of the following:

a) num1 = 4

num2 = num1 + 1

print (num1, num2)

b) num1, num2 = 2, 6

num1, num2 = num2, num1 + 2

c) num1, num2 = 2, 3

num3, num2 = num1, num3 + 1

print (num1, num2, num3)

Output: 2,5

Output: 6,4

Output: error

Question 6. Which data type will be used to represent the following data values and why?

a) Number of months in a year

b) Resident of Delhi or not

c) Mobile number

d) Pocket money

e) Volume of a sphere

f) Perimeter of a square

g) Name of the student

h) Address of the student

Question 7. Give the output of the following when num1 = 4, num2 = 3, num3 = 2

a) num1 += num2 + num3

print (num1)

b) num1 = num1 ** (num2 + num3)

c) num1 **= num2 + num3

d) num1 = ‘5’ + ‘5’

print(num1)

e) print(4.00/(2.0+2.0))

f) num1 = 2+9*((3*12)-8)/10

g) num1 = 24 // 4 // 2

h) num1 = float(10)

i) num1 = int(‘3.14’)

j) print(‘Bye’ == ‘BYE’)

k) print(10 != 9 and 20 >= 20)

l) print(10 + 6 * 2 ** 2 != 9//4 -3 and 29

>= 29/9)

m) print(5 % 10 + 10 < 50 and 29 <= 29)

n) print((0 < 6) or (not(10 == 6) and

(10<0)))

Output:1024

Output:27.2

Output:10.0

Output: False

Output:True

Output: True

Question 8. Categorise the following as syntax error, logical error or runtime error:

b) num1 = 25; num2 = 0; num1/num2

a) 25 / 0 :- Runtime Error, because of divisible by zero

b) num1 = 25; num2 = 0; num1/num2 :- Runtime Error, because of divisible by zero

Question 9. A dartboard of radius 10 units and the wall it is hanging on are represented using a two-dimensional coordinate system, with the board’s center at coordinate (0,0). Variables x and y store the x-coordinate and the y-coordinate of a dart that hits the dartboard. Write a Python expression using variables x and y that evaluates to True if the dart hits (is within) the dartboard, and then evaluate the expression for these dart coordinates:

In case you are missed :- Previous Chapter Solution

Question 10. Write a Python program to convert temperature in degree Celsius to degree Fahrenheit. If water boils at 100 degree C and freezes as 0 degree C, use the program to find out what is the boiling point and freezing point of water on the Fahrenheit scale. (Hint: T(°F) = T(°C) × 9/5 + 32)

deffar_conv(t):

x=t*9/5 + 32

print(far_conv(100))

Question 11 . Write a Python program to calculate the amount payable if money has been lent on simple interest. Notes Ch 5.indd 117 08-Apr-19 12:35:13 PM 2020-21 118 Computer Science – Class xi Principal or money lent = P, Rate of interest = R% per annum and Time = T years. Then Simple Interest (SI) = (P x R x T)/ 100. Amount payable = Principal + SI. P, R and T are given as input to the program.

principal=int(input(“P=”))

rate=int(input(“I=”))

time=int(input(“T=”))

defamount_pay(principal,rate,time):

simple_intrest=(principal*rate*time)/100

TOTAL_amount=Print+simple_intrest

returnTOTAL_amount

print(“Total Payble amount”)

print(amount_pay(principal,rate,time))

Question 12. Write a program to calculate in how many days a work will be completed by three persons A, B and C together. A, B, C take x days, y days and z days respectively to do the job alone. The formula to calculate the number of days if they work together is xyz/(xy + yz + xz) days where x, y, and z are given as input to the program.

x=int(input(“x=”))

y=int(input(“Y=”))

z=int(input(“Y=”))

defwork_days(x,y,z):

days=x*y*z/(x*y+y*z+z*x)

return days

print(“Work will complet(in days)”)

print(work_days(x,y,z))

Question 13. Write a program to enter two integers and perform all arithmetic operations on them.

a=int(input(“Enter First Number: “))

b=int(input(“Enter Second Number: “))

defAddtion(a,b):

def subtraction(a,b):

def multiplication(a,b):

def division(a,b):

print(“Addtion of {0} & {1} is : “.format(a,b))

print(Addtion(a,b))

print(“subtraction of {0} & {1} is : “.format(a,b))

print(subtraction(a,b))

print(“multiplicationof {0} & {1} is : “.format(a,b))

print(multiplication(a,b))

print(“division of {0} & {1} is : “.format(a,b))

print(division(a,b))

Question14. Write a program to swap two numbers using a third variable.

first_number=int(input(“Enter First Number: “))

second_number=int(input(“Enter Second Number: “))

def swap(first_number,second_number):

third_variable=first_number

first_number=second_number

second_number=third_variable

returnfirst_number,second_number

print(swap(first_number,second_number))

Question 15.  Write a program to swap two numbers without using a third variable.

first_number,second_number=second_number,first_number

Question 16. Write a program to repeat the string ‘‘GOOD MORNING” n times. Here ‘n’ is an integer entered by the user.

n=int(input(“Enter Number: “))

fori in range(n):

print(“GOOD MORINING “)

Question 17. Write a program to find average of three numbers.

x=int(input(“Enter First Number: “))

y=int(input(“Enter Second Number: “))

z=int(input(“Enter Third Number: “))

def  average(x,y,z):

avg=x+y+z/3

print(“Average : “)

print(average(x,y,z))

Question 18. The volume of a sphere with radius r is 4/3πr3. Write a Python program to find the volume of spheres with radius 7cm, 12cm, 16cm, respectively.

defvolume_sphere(r):

pi=3.1415926535897931

volume=4.0/3.0*pi* r**3

return volume

print(“volume of spheres with radius 7cm”)

print(volume_sphere(7))

print(“volume of spheres with radius 12cm”)

print(volume_sphere(12))

print(“volume of spheres with radius 16cm”)

print(volume_sphere(16))

Question 19. Write a program that asks the user to enter their name and age. Print a message addressed to the user that tells the user the year in which they will turn 100 years old.

fromdatetime import datetime

name = input(‘Name \n’)

age = int(input(‘Age  \n’))

defhundred_year(age):

hundred = int((100-age) + datetime.now().year)

return hundred

x=hundred_year(age)

print (‘Hello %s.  You will turn 100 years old in %s.’ % (name,x))

Question 20. The formula E = mc2 states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3×108 m/s) squared. Write a program that accepts the mass of an object and determines its energy.

m=int(input(“Enter Mass in Kg: “))

def Einstein(m):

c=299792458

print(“Equivalent energy (E): “)

print(Einstein(m))

Question 21. Presume that a ladder is put upright against a wall. Let variables length and angle store the length of the ladder and the angle that it forms with the ground as it leans against the wall. Write a Python program to compute the height reached by the ladder on the wall for the following values of length and angle:

a)16 feet and 75 degrees

b)20 feet and 0 degrees

c)24 feet and 45 degrees

d)24 feet and 80 degrees

import math

defheight_reched(length,degrees):

radian=math.radians(degrees)

sin=math.sin(radian)

height=round(length*sin,2)

return height

print(” height reached by the ladder on the wall for the  length is 16 feet and 75 degrees “)

print(height_reched(16,75))

print(” height reached by the ladder on the wall for the  length is 20 feet and 0 degrees “)

print(height_reched(20,0))

print(” height reached by the ladder on the wall for the  length is 24 feet and 45 degrees “)

print(height_reched(24,45))

print(” height reached by the ladder on the wall for the  length is 24 feet and 80 degrees “)

print(height_reched(24,80))

In case you are missed :- Next Chapter Solution

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Solutions of Computer Science with Python by Sumita Arora for Class 11 CBSE & NCERT

Computer science, 2023-24 syllabus.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 11 Physics Assignments

We have provided below free printable Class 11 Physics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 11 Physics . These Assignments for Grade 11 Physics cover all important topics which can come in your standard 11 tests and examinations. Free printable Assignments for CBSE Class 11 Physics , school and class assignments, and practice test papers have been designed by our highly experienced class 11 faculty. You can free download CBSE NCERT printable Assignments for Physics Class 11 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Physics Class 11. Students can click on the links below and download all Pdf Assignments for Physics class 11 for free. All latest Kendriya Vidyalaya Class 11 Physics Assignments with Answers and test papers are given below.

Physics Class 11 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 11 Physics . Students and teachers can download and save all free Physics assignments in Pdf for grade 11th. Our expert faculty have covered Class 11 important questions and answers for Physics as per the latest syllabus for the current academic year. All test papers and question banks for Class 11 Physics and CBSE Assignments for Physics Class 11 will be really helpful for standard 11th students to prepare for the class tests and school examinations. Class 11th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 11 Physics Download in Pdf

Advantages of Class 11 Physics Assignments

• As we have the best and largest collection of Physics assignments for Grade 11, you will be able to easily get full list of solved important questions which can come in your examinations.
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• Class 11 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Physics chapter wise worksheets and assignments for free in Pdf
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We provide here Standard 11 Physics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Physics in Grade 11, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

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We have provided the best collection of question bank and practice tests for Class 11 for all subjects. You can download them all and use them offline without the internet.

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• NCERT Solutions
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• Chapter 5: Complex Numbers And Quadratic Equations

NCERT Solutions For Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

Ncert solutions class 11 maths chapter 5 – free pdf download.

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 4.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are prepared by the expert teachers at BYJU’S. These NCERT Solutions of Maths help students in solving problems quickly, accurately and efficiently. Also, BYJU’S provides step-by-step solutions for all NCERT problems, thereby ensuring students understand them and clear their board exams with flying colours. The chapter Complex Numbers and Quadratic Equations is categorised under the CBSE Syllabus for 2023-24 and includes different critical Mathematical theorems and formulae. The NCERT textbook has many practice problems to cover all these concepts, which would help students easily understand higher concepts in future. BYJU’S provides solutions for all these problems with proper explanations. These NCERT Solutions from BYJU’S help students who aim to clear their exams even with last-minute preparations. However, NCERT Solutions for Class 11 Maths are focused on mastering the concepts along with gaining broader knowledge.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

Access answers of maths ncert class 11 chapter 5 – complex numbers and quadratic equations.

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Access the exercises of Maths NCERT Class 11 Chapter 5

Exercise 5.1 Solutions 14 Questions Exercise 5.2 Solutions 8 Questions Exercise 5.3 Solutions 10 Questions Miscellaneous Exercise on Chapter 5 Solutions 20 Questions; the summarisation of the topics discussed in Chapter 5 of the Class 11 NCERT curriculum is listed below.

Access NCERT Solutions for Class 11 Maths Chapter 5

Exercise 5.1 Page No: 103

Express each of the complex numbers given in Exercises 1 to 10 in the form a + ib.

1. (5i) (-3/5i)

(5i) (-3/5i) = 5 x (-3/5) x i 2

(5i) (-3/5i) = 3 + i0

2. i 9 + i 19

i 9 + i 19 = (i 2 ) 4 . i + (i 2 ) 9 . i

= (-1) 4 . i + (-1) 9 .i

= 1 x i + -1 x i

i 9 + i 19 = 0 + i0

Now, multiplying the numerator and denominator by i we get

i -39 = 1 x i / (-i x i)

i -39 = 0 + i

4. 3(7 +  i 7) +  i (7 +  i 7)

3(7 +  i 7) +  i (7 +  i 7) = 21 + i 21 + i 7 + i 2 7

= 14 + i 28

3(7 +  i 7) +  i (7 +  i 7) = 14 + i 28

5. (1 –  i ) – (–1 +  i 6)

(1 –  i ) – (–1 +  i 6) = 1 –  i + 1 –  i 6

(1 –  i ) – (–1 +  i 6) = 2 – i 7

8. (1 –  i ) 4

(1 –  i ) 4 = [(1 –  i ) 2 ] 2

= [1 + i 2 – 2 i ] 2

Hence, (1 –  i ) 4 = -4 + 0 i

9. (1/3 + 3 i ) 3

Hence, (1/3 + 3 i ) 3 = -242/27 – 26 i

10. (-2 – 1/3 i ) 3

(-2 – 1/3 i ) 3 = -22/3 – 107/27 i

Find the multiplicative inverse of each of the complex numbers given in Exercises 11 to 13.

Let’s consider z  = 4 – 3 i

= 4 + 3 i  and

|z| 2 = 4 2 + (-3) 2 = 16 + 9 = 25

Thus, the multiplicative inverse of 4 – 3 i  is given by z -1

12. √5 + 3 i

Let’s consider  z  = √5 + 3 i

|z| 2 = (√5) 2 + 3 2 = 5 + 9 = 14

Thus, the multiplicative inverse of √5 + 3 i is given by z -1

Let’s consider  z  = – i

Thus, the multiplicative inverse of – i  is given by z -1

14. Express the following expression in the form of a + ib:

Exercise 5.2 Page No: 108

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.

1. z = – 1 – i √3

2. z = -√3 + i

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Exercise 5.3 Page No: 109

Solve each of the following equations:

1. x 2 + 3 = 0

Given the quadratic equation,

x 2  + 3 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we have

a  = 1,  b  = 0, and  c  = 3

So, the discriminant of the given equation will be

D =  b 2  – 4 ac  = 0 2  – 4 × 1 × 3 = –12

Hence, the required solutions are

2. 2x 2 + x + 1 = 0

2 x 2  +  x  + 1 = 0

a  = 2,  b  = 1, and  c  = 1

D =  b 2  – 4 ac  = 1 2  – 4 × 2 × 1 = 1 – 8 = –7

3. x 2 + 3x + 9 = 0

x 2  + 3 x  + 9 = 0

a  = 1,  b  = 3, and  c  = 9

D =  b 2  – 4 ac  = 3 2  – 4 × 1 × 9 = 9 – 36 = –27

4. – x 2  +  x  – 2 = 0

– x 2  +  x  – 2 = 0

a  = –1,  b  = 1, and  c  = –2

D =  b 2  – 4 ac  = 1 2  – 4 × (–1) × (–2) = 1 – 8 = –7

5. x 2  + 3 x  + 5 = 0

x 2  + 3 x  + 5 = 0

a  = 1,  b  = 3, and  c  = 5

D =  b 2  – 4 ac  = 3 2  – 4 × 1 × 5 =9 – 20 = –11

6. x 2  –  x  + 2 = 0

x 2  –  x  + 2 = 0

a  = 1,  b  = –1, and  c  = 2

So, the discriminant of the given equation is

D =  b 2  – 4 ac  = (–1) 2  – 4 × 1 × 2 = 1 – 8 = –7

7. √2 x 2  + x  + √2 = 0

√2 x 2  + x  + √2 = 0

a  = √2,  b  = 1, and  c  = √2

D =  b 2  – 4 ac  = (1) 2  – 4 × √2 × √2 = 1 – 8 = –7

8. √3 x 2  – √2 x  + 3√3 = 0

√3 x 2  – √2 x  + 3√3 = 0

a  = √3,  b  = -√2, and  c  = 3√3

D =  b 2  – 4 ac  = (-√2) 2  – 4 × √3 × 3√3 = 2 – 36 = –34

9. x 2  + x  + 1/√2 = 0

x 2  + x  + 1/√2 = 0

It can be rewritten as,

√2 x 2  + √2 x  + 1 = 0

a  = √2,  b  = √2, and  c  = 1

D =  b 2  – 4 ac  = (√2) 2  – 4 × √2 × 1 = 2 – 4√2 = 2(1 – 2√2)

10. x 2  + x /√2 + 1 = 0

x 2  + x /√2 + 1 = 0

D =  b 2  – 4 ac  = (1) 2  – 4 × √2 × √2 = 1 – 8 = -7

Miscellaneous Exercise Page No: 112

2. For any two complex numbers   z 1  and z 2 , prove that

Re (z 1 z 2 )   = Re z 1  Re z 2  – Im z 1  Im z 2

3. Reduce to the standard form.

5. Convert the following into the polar form:

Solve each of the equations in Exercises 6 to 9.

6. 3x 2 – 4x + 20/3 = 0

Given the quadratic equation, 3x 2 – 4x + 20/3 = 0

It can be re-written as: 9x 2 – 12x + 20 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we get

a  = 9,  b  = –12, and  c  = 20

D =  b 2  – 4 ac  = (–12) 2  – 4 × 9 × 20 = 144 – 720 = –576

7. x 2 – 2x + 3/2 = 0

Given the quadratic equation, x 2 – 2x + 3/2 = 0

It can be re-written as 2x 2 – 4x + 3 = 0

a  = 2,  b  = –4, and  c  = 3

D =  b 2  – 4 ac  = (–4) 2  – 4 × 2 × 3 = 16 – 24 = –8

8. 27x 2 – 10x + 1 = 0

Given the quadratic equation, 27 x 2  – 10 x  + 1 = 0

a  = 27,  b  = –10, and  c  = 1

D =  b 2  – 4 ac  = (–10) 2  – 4 × 27 × 1 = 100 – 108 = –8

9. 21x 2 – 28x + 10 = 0

Given the quadratic equation, 21 x 2  – 28 x  + 10 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we have

a  = 21,  b  = –28, and  c  = 10

D =  b 2  – 4 ac  = (–28) 2  – 4 × 21 × 10 = 784 – 840 = –56

10. If z 1 = 2 – i , z 2 = 1 + i , find

Given, z 1 = 2 – i , z 2 = 1 + i

12. Let z 1 = 2 – i , z 2 = -2 + i . Find

13. Find the modulus and argument of the complex number.

14. Find the real numbers  x  and  y  if ( x  –  iy ) (3 + 5 i ) is the conjugate of – 6 – 24 i .

Let’s assume z = ( x  –  iy ) (3 + 5 i )

(3x + 5y) – i (5x – 3y) = -6 -24 i

On equating real and imaginary parts, we have

3x + 5y = -6 …… (i)

5x – 3y = 24 …… (ii)

Performing (i) x 3 + (ii) x 5, we get

(9x + 15y) + (25x – 15y) = -18 + 120

x = 102/34 = 3

Putting the value of  x  in equation (i), we get

3(3) + 5y = -6

5y = -6 – 9 = -15

Therefore, the values of  x  and  y are 3 and –3, respectively.

15. Find the modulus of

16. If ( x  +  iy ) 3  =  u  +  iv , then show that

17. If α and β are different complex numbers with |β| = 1, then find

18. Find the number of non-zero integral solutions of the equation |1 – i| x = 2 x.

Therefore, 0 is the only integral solution of the given equation.

Hence, the number of non-zero integral solutions of the given equation is 0.

19. If ( a  +  ib ) ( c  +  id ) ( e  +  if ) ( g  +  ih ) = A +  i B, then show that

( a 2  +  b 2 ) ( c 2  +  d 2 ) ( e 2  +  f 2 ) ( g 2  +  h 2 ) = A 2  + B 2

20. If, then find the least positive integral value of  m .

Thus, the least positive integer is 1.

Therefore, the least positive integral value of  m  is 4 (= 4 × 1).

NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

Chapter 5 of Class 11 Complex Numbers and Quadratic Equations has 3 exercises and a miscellaneous exercise to help the students practise the required number of problems to understand all the concepts. The topics and sub-topics discussed in the PDF of NCERT Solutions for Class 11 of this chapter include 5.1 Introduction We know that some of the quadratic equations have no real solutions. That means the solution of such equations includes complex numbers. Here, we have found the solution of a quadratic equation ax 2 + bx + c = 0 where D = b 2 – 4ac < 0. 5.2 Complex Numbers Definition of complex numbers, examples and explanations about the real and imaginary parts of complex numbers have been discussed in this section. Class 11 Maths NCERT Supplementary Exercise Solutions PDF helps the students to understand the questions in detail. 5.3 Algebra of Complex Numbers 5.3.1 Addition of two complex numbers

5.3.2 Difference of two complex numbers

5.3.3 Multiplication of two complex numbers

5.3.4 Division of two complex number

5.3.5 Power of i

5.3.6 The square roots of a negative real number

5.3.7 Identities

After studying these exercises, students are able to understand the basic BODMAS operations on complex numbers, along with their properties, power of i, square root of a negative real number and identities of complex numbers. 5.4 The Modulus and the Conjugate of a Complex Number The detailed explanation provides the modulus and conjugate of a complex number with solved examples. 5.5 Argand Plane and Polar Representation 5.5.1 Polar representation of a complex number

In this section, it has been explained how to write the ordered pairs for the given complex numbers, the definition of a Complex plane or Argand plane and the polar representation of the ordered pairs in terms of complex numbers.

• A number of the form a + ib, where a and b are real numbers, is called a complex number, “ a” is called the real part, and “ b” is called the imaginary part of the complex number
• z 1 + z 2 = (a + c) + i (b + d)
• z 1 z 2 = (ac – bd) + i (ad + bc)
• For any non-zero complex number z = a + ib (a ≠ 0, b ≠ 0), there exists a complex number, denoted by 1/z or z–1, called the multiplicative inverse of z
• For any integer k, i 4k = 1, i 4k + 1 = i, i 4k + 2 = – 1, i 4k + 3 = – i
• The polar form of the complex number z = x + iy is r (cosθ + i sinθ)
• A polynomial equation of n degree has n roots.

Disclaimer – 

Dropped Topics – 

5.5.1 Polar Representation of a Complex Number 5.6 Quadratic Equation Example 11 and Exercise 5.3 Examples 13, 15, 16 Ques. 5–8, 9 and 13 (Miscellaneous Exercise) Last three points in the Summary 5.7 Square-root of a Complex Number

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Important Questions for CBSE Class 11 Business Studies Chapter 5 – Emerging Modes of Business

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Important Questions Class 11 Business Studies Chapter 5 – Emerging Modes of Business

Business Studies can be characterized as a set of interconnected business disciplines that result in different fundamental knowledge and abilities. It is a type of subject that focuses on the essential information and abilities needed to organize businesses and general office management. Emerging modes of business are the fifth chapter of the Class 11th syllabus, which teaches about different modes of business. This chapter covers concepts such as the meaning of e-business, the process of online buying and selling, distinguishing e-business from traditional business, the benefits of switching to electronic mode, significant security concerns of e-business, the need for business processing outsourcing, and so on. This chapter carries significant weightage in the Business Studies syllabus. Students can easily access Chapter 5 Class 11 Business Studies Important Questions and more from the Extramarks’ website. 

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It is vital to review all chapters in the Business Studies syllabus thoroughly. At Extramarks, we understand the value of solving essential questions. Keeping that in mind, we have curated a list of important questions from different sources such as the NCERT Textbook, NCERT Exemplar, other reference books, past years’ exam papers, and so on. After much research, our Business Studies subject matter experts have developed step-by-step solutions to help students to comprehend the topics in a better way. Students can register with Extramarks and access Important Questions Class 11 Business Studies Chapter 5.

Along with Business Studies Class 11 Chapter 5 Important Questions, there is so much that the Extramarks’ website has to offer. Students can easily find materials like NCERT Solutions, CBSE revision notes , past years’ question papers, NCERT books, and more on the Extramarks’ website.

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Emerging Modes of Business Class 11 Questions and Answers

A team of Extramarks Business Studies experts has developed an entire list of Class 11 Business Studies Chapter 5 Important Questions taking references from numerous primary and secondary sources. These questions include a wide variety of topics as follows:

The meaning of e-business

The process of online buying and selling

Distinguishing e-business from traditional business

Benefits of switching to electronic mode

Significant security concerns of e-business

Need for business processing outsourcing.

These questions and their solutions help students to comprehend Emerging Modes of Business.

Given below are a few Important Questions from Class 11 Business Studies Chapter 5 and their solutions:

Q1. Briefly describe the data storage and transmission risks in e-business.

Answer. Data is exposed to various threats when it is being kept or transferred. With the help of hackers or viruses, it is possible for crucial information to be taken or maliciously manipulated. As a result of such activities, data may be corrupted. The transmission of online transactions is likewise potentially very dangerous. When data is transferred through the Internet, the following dangers can occur.

• If a vendor or buyer denies that an order was made on their behalf.
• Goods may be delivered to an incorrect address or may not arrive at all.
• In other circumstances, the seller claims not to have received the payment, despite deducting it from the receiver’s account.

Q2. What exactly does the term “intra-B Commerce” mean?

Answer. Intra-B Commerce is a type of e-commerce in which the parties participating in the electronic transactions are from the same company. Today’s enterprises can engage in flexible manufacturing partly because of intra-B commerce. Computer networks allow the marketing department to connect with the manufacturing department constantly, allowing tailored goods to be created based on the demands of each consumer.

Employees might, for example, use Virtual Private Network (VPN) technology to avoid having to come into the workplace. Instead, the workplace comes to them, and they may work on their schedule from anywhere, at any time.

Q3. State any three differences between e-business and traditional business.

Answer. The listing below three differences between e-business and traditional business:

E-business:

• It’s challenging to start a firm since there are so many requirements.
• The initial cost is significant.
• It is solely limited to the region where it is established.

Traditional business:

• It’s simple to set up.
• Setup costs are minimal.
• Because everyone is linked on the Internet, you can contact individuals nationwide.

Q4. Explain what the term “e-business” means.

Answer. E-business (Electronic business) is the practice of conducting business through the Internet. It entails not just purchasing and selling but also providing customer service and cooperating with other businesses. E-commerce is the future for all businesses. It refers to using technology, processes, and management techniques to improve organisational competitiveness through the strategic use of electronic data.

It goes beyond e-commerce by tightly integrating e-commerce with company processes to enhance performance, create value, and allow new business-to-customer connections. It entails improving customer and supplier connections. Checking the competition is helpful, generating fresh product ideas and suppliers. Its primary focus is on re-engineering corporate processes.

Q5. Discuss the limitations of the electronic mode of doing business. Are these limitations severe enough to restrict its scope? Give reasons for your answer.

Answer. The following are some of the electronic methods of business drawbacks:

Delivery Time:

• In the world of e-commerce, goods delivery takes time and this really impacts customers and turns them off. 
• These days, however, e-businesses are attempting to tackle such concerns by offering a concise time frame. Amazon, for example, now guarantees one-day delivery.

 Technological capability and competency of e-business participants are needed:

• T he parties participating in e-business must have a high level of computer literacy. The so-called digital gap can also be attributed to this requirement.
• The phrase “digital divide” refers to societal divisions depending on one’s familiarity with or lack of familiarity with digital technology.

Ethical fallouts:

• Companies use an ‘electronic eye’ to watch your computer files, email account, and internet visits, among other things, to learn about your likes, preferences, and other information. In a variety of respects, it’s immoral.

Security issues:

• Many people can conduct business online. Hackers also have an easier time getting a person’s financial information. It has a few security and integrity issues. This causes potential clients to be sceptical.

Lack of personal touch:

• You can’t touch or feel the product, unlike in traditional business. As a result, customers can’t assess the product’s quality until the order has been delivered.
• Traditional companies have traditional touch with salespeople, and as a result, there is a sense of compassion and trustworthiness. It also increases consumer trust. In an e-business paradigm, such features will always be absent.

Q6. What exactly do you mean when you say:

• B2B Commerce
• B2C Commerce
• Intra-B Commerce
• C2C Commerce

Answer: The terms are explained below:

B2B Commerce:

• The name B2B (business-to-business) was coined since both parties participating in e-commerce transactions are companies.
• To provide utility or offer value, a company must collaborate with several other companies. These companies might be input suppliers or vendors or be part of the distribution channel via which a corporation sells its products to customers.
• For instance, turtle.com.

B2C Commerce:

• Commercial-to-customer (B2C) contacts bring together businesses and their consumers.
• It covers various online marketing tasks, including finding activities, promoting them, and, on rare occasions, even delivering products.
• It allows a company to communicate with its clients 24 hours a day, seven days a week, which aids in determining customer satisfaction levels.
• For instance, Amazon, Nykaa, and others.

Intra-B Commerce:

• The parties involved in electronic transactions are all employees of the same firm.
• Intra-B trade allows today’s enterprises to engage in flexible production to a large extent. Computer networks allow the marketing department to connect with the manufacturing department constantly, allowing tailored goods to be created based on the demands of each consumer.
• Customised mobile phone and laptop manufacturing, for example, need collaboration across several divisions inside a company.

C2C Commerce:

• The customer is the origin of the business, and the customer is the final goal.
• This type of business is ideal for dealing with commodities without an established market mechanism.
• For instance, eBay, Etsy, and other such sites.

Q7. Why are e-business and Outsourcing referred to as the emerging modes of business? Discuss the factors responsible for the growing importance of these trends.

Answer. In the recent decade, the business has undergone significant transformations and evolved. The method of business refers to how a company conducts its operations. E-business and Outsourcing are referred to as emergent business models since they have revolutionised the way businesses are conducted. E-business is the practice of conducting business through the Internet. It uses the Internet to communicate with customers and suppliers. Some E-business work includes Inventory management, warehousing, software development, and other electronic commerce forms.

Outsourcing is the process of an organisation’s non-core operations being delegated to another organisation with competence in those areas. It lowers the company’s expenditure for keeping such individuals on staff. The experience, efficiency, and improved calibre of employees benefit an organisation.

Here are some of the causes that are contributing to the growing prominence of such trends:

• Improvements in corporate processes have resulted from new ways of working and innovation.
• Consumers are more aware, and there is a greater desire for higher quality, lower prices, and better customer service.
• Businesses must grow with new technology, making them more scalable.

Q8. What are the numerous applications and advantages of e-commerce?

Answer. Following are the advantages and applications of e-commerce:

• Before sale inquiry: Customers can contact the firm’s sales professionals via the corporate website to obtain information about the product’s pricing, specifications, and other details. It may choose a merchant based on advertising or a suggestion from a friend.
• Customers search: E-commerce helps identify potential customers for a product or service by sending them informational emails about the product or service. These emails assist clients in comprehending the product and deciding whether to purchase it. It uses a search engine to locate a suitable seller’s website.
• Sales promotions: Online trade on the Internet may boost sales while also allowing for improved customer service by collecting complaints via email.
• Publication and distribution of information on the company’s website assists in delivering up-to-date information on the product’s pricing, discount, and quality, among other things. The website may be visited from anywhere on the planet.
• Product promotion: E-commerce facilitates product promotion through emails, websites, telemarketing, and other means. Customers can receive the most up-to-date information via email or the company’s website.
• Product sales: Products can be purchased online through the website. Customers may select a product from a picture catalogue and place an order online. You can pay with a check, a draught, or a credit card.
• After-sales service: Customers may receive prompt after-sales support by contacting them using the email address. Customers can send concerns to the company via email.
• Purchasing goods: Suppliers can be identified on the Internet for a particular product or service. Suppliers from all around the world may be found using search engines like Google and Yahoo.
• Money transfer: Internet banking allows you to move money from one bank to another. Customers are given a safe identity to conduct online transactions. Payment can be made online using a credit card or a check.

Q9. What are the ethical concerns involved in Outsourcing?

Answer. Outsourcing has also brought up specific ethical issues. The following are the primary ethical concerns:

• Discrimination: Similarly, pay discrimination arises based on the worker’s sex. Women are paid lesser salaries because workers are exploited by paying less than the minimum wage.
• Employment: When a function is outsourced to a firm in another nation, it eliminates job prospects in one’s own country.
• Child labour: Outsourcing has resulted in the employment of children and women in factories, where working conditions are unclean and even deadly. Corporations cannot do so due to tight restrictions prohibiting the use of child labour in industrialised countries.
• Confidentiality: Outsourcing entails the interchange of vital information and expertise, so confidentiality concerns have been expressed and need to be addressed. It can be detrimental to the interests of the party that outsources its procedures, and there is even a chance that competing corporations will gain access to information about that company. 

Q10. How does Outsourcing represent a new model of business?

Answer. Outsourcing has revolutionised the way companies are conducted in the past, and it continues to expand every day. It also has a bright future ahead of it. Outsourcing is a cutting-edge idea that has increased enterprises’ value, convenience, and efficiency in procurement, manufacturing, and marketing. Therefore, it is referred to as an emergent business model.

The following are the variables that have contributed to outsourcing’s increased importance:

• Assist in lowering costs for high-quality goods.
• Facilitate the advancement of technology and innovation.
• Increase the speed of the business process.
• Help businesses focus on core areas of expertise, and master that.

Q11. In e-business, what does the letter ‘e’ stand for?

Answer. In e-business, the letter ‘E’ stands for electronic. Using computer networks to conduct business, trade, and commerce is referred to as e-business. E-business is a broader term that refers to various electronic business activities and services, including well-known e-commerce transactions.

Q12. Discuss the salient aspects of B2C Commerce.

Answer. The following are some of the essential characteristics of B2C commerce:

• With the help of regional and worldwide support centres, customers can access 24 hours a day, 7 days a week.
• Products may be advertised across geographies, reaching a more significant number of people.
• Advertising is less expensive since it can be done utilising online promotional platforms like social media and websites.
• Customers can pay using various methods, including debit cards, credit cards, net banking, or cash on delivery, and there are also attractive EMI options available.
• Customers can have items tailored to their preferences and interests.

Q13. What are the three advantages of doing business online?

Answer. The following are three advantages of doing business online:

• Speed and efficiency: Online ordering systems can handle payments and orders in real-time, which is typically faster, more precise, and less expensive than human workers.
• There are no geographical limitations: anyone can order anything anytime. On the one hand, the online business provides access to the worldwide market for the seller, while on the other hand, it allows the buyer to choose items from nearly any part of the world.
• Flexible Working Hours: Because the Internet is always on, you may establish your working hours. E-business overcomes the time constraints that location-based businesses encounter.

Q14. Elaborate on the steps involved in online trading.

Answer. The steps involved in online trading are: Registration, Placing an order and the payment mechanism.

Registration:

• You create an ‘account’ when you register with an online merchant by filling out the registration form.
• Because the regions linked to an individual’s “account” and “shopping basket” are password-protected, a “password” must be entered among the other information.

Placing an order:

• By dragging and dropping items into the shopping basket, you may add them to the cart.
• A shopping cart is like an online record of a customer’s items in his basket when shopping on the Internet.
• You can ‘checkout’ once you’ve selected what you want to buy.

Payment mechanism: Online purchases can be made in various ways.

• Net-banking Transfer: Modern banks offer their clients the option of transferring payments electronically through the Internet using the Immediate Payment Service (IMPS), NEFT, and RTGS.
• Cash-on-Delivery: When you order anything online, you may pay for it with cash when it arrives.
• Cheque: The online retailer may arrange for the customer’s cheque to be picked up. Product delivery may be tried after realisation.
• Credit or Debit Cards: Credit card holders can use their cards to make purchases on credit. The card issuing bank assumes the amount due by the cardholder to the online seller and subsequently transfers the transaction’s amount to the seller’s credit.

The bearer of a debit card can make purchases up to the amount of money in the connected account. The amount owed as payment is debited electronically from the card at the time of the transaction.

• Digital cash: Digital Cash has no physical properties, but it allows you to use actual money electronically, such as through e-wallets like Paytm.

Q15. Write a short note on the different types of Outsourcing.

Answer. Businesses can use Outsourcing for any non-core company process. The following are examples of popular services that may be outsourced:

• Advertising: All large corporations delegate the task of publicising their products and services to specialist organisations. Advertising companies are often entrusted with planning, producing, and spreading ads for businesses’ products and services. Coca-Cola, Pepsi, Hindustan Lever, and other significant marketers deal with advertising firms. The advertising agency agrees to supply all advertising services in exchange for a fee under the terms of the agreement. Outsourcing also facilitates the usage of ad-agency professionals’ services.
• Financial Services: Large corporations require financial services from internal and external sources. Every business needs financial services, such as payroll accounting, merchant banking, underwriting, etc.

Except for huge companies, manufacturing and commercial organisations find it easier and more cost-effective to rely on outside financial institutions for different financial services. Reliance Industries, for example, may outsource financial services such as issuing ADRs/GDRs in overseas capital markets to HSBC Bank.

• Customer Support Service: ‘A customer is like a valuable ornament that should not be taken by anybody else,’ says Customer Support Service (CSS). Customers may make use of a variety of services to help them buy and use items. Companies are learning that providing good customer service is an excellent approach to competitive advantage in today’s market.

Customers require home delivery, consumer durables repair and maintenance, and information and counselling on alternative brands that best match their requirements. Customer support services can be outsourced so that businesses can focus on sales. For example, GE Capital and other corporations have built contact centres in India to help consumers in many nations.

• Courier Service: Big corporations must ship large quantities of mail, packages, and other items. They employ sendees from courier companies like DTH, Overnight Express, and others. These courier companies acquire all items deposited from client offices and deliver them to their destinations. Clients benefit from courier service since it is faster, more efficient, cheaper, more dependable, and individualised.

Q16. Describe briefly any two applications of e-business.

Answer. The following are some of the applications of e-business:

• E-delivery: This procedure entails the electronic transmission of movies, games, or software straight to the consumer’s system using high-speed data services. Payments are made over the Internet.
• E-procurement: This refers to web-based transactions between businesses that are either buyers or sellers. Reverse auctions are also used in transactions where numerous vendors compete to sell their products to a single buyer. There are numerous players in a digital marketplace, such as several buyers and sellers or a single vendor.

Q17. Evaluate the need for Outsourcing and discuss its limitations.

Answer. Contracting some corporate tasks to external firms is known as Outsourcing. Following are the need for Outsourcing:

The pursuit of excellence:

• Outsourcing helps the organisation to strive for excellence in two ways. Individuals flourish in the tasks they can accomplish because of their tight concentration.
• They also succeed by expanding their skills by delegating the remaining work to people who are skilled in those areas.

Limiting the scope of a company’s operations:

• Businesses realise the value of concentrating on only a few areas with unique capabilities or core competencies and contracting out the rest of the tasks to their outsourcing partners.
• They may focus their time and resources on a few essential activities by limiting the scope of their firm and increasing efficiency and effectiveness.

Partnerships for Growth:

• The investment needs are minimised to the extent that one can use the services of others.
• As a result, a business may expand swiftly since the same amount of investible money can be used to develop many businesses.
• Outsourcing facilitates inter-organisational information exchange and collaborative learning.

Development of the economy:

• Outsourcing, particularly offshore Outsourcing, encourages entrepreneurship, job creation, and exports in the host nations (i.e., countries where Outsourcing is done).

Cost-cutting:

• Specialisation and division of labour Quality may be improved while expenses are reduced.
• Outsourcing partners take advantage of economies of scale by delivering the same service to many organisations.
• Differences in the prices of key industrial inputs among nations can help reduce costs.

Some limitations of Outsourcing are:

Sweat shopping:

• Outsourcing tries to save costs by utilising low-cost labour as much as possible.
• As a result, companies that outsource search for ‘doing’ talents rather than developing ‘thinking’ skills.

Concerns of ethics:

• To save money, businesses outsource their labour to another nation, where it is performed in an unethical manner.
• Working with children, for example, is a viable option.

Intense resentment in native countries:

• What is eventually outsourced while contracting out manufacturing, marketing, research and development, or IT-based services is ’employment’ or jobs from one nation to another.
• If the home nation is dealing with an unemployment issue, this might lead to resentment.

Confidentiality: 

• Outsourcing entails the interchange of a lot of essential data and expertise.
• It can harm the interests of the party that outsources its procedures, and there is even a chance that competing corporations will gain access to information about that company.

Q18. Why are e-commerce and outsourcing referred to as developing business models? What are the elements that are causing these trends to become more important?

Answer. E-business and Outsourcing have transformed the way businesses are conducted in the past, and they continue to expand daily, with a bright future ahead of them. E-businesses and Outsourcing are creative concepts that have increased enterprises’ value, convenience, and efficiency in company operations such as procurement, manufacturing, and marketing, among others. This is why they are referred to be emergent business models:

Outsourcing and e-business are becoming increasingly important due to the following factors:

• Facilitate technological development and innovation: Any company must innovate and create new ideas and products to remain competitive. In this environment, e-business and outsourcing have proven to be a godsend for manufacturers, as they allow for the continuous development of firm strategy and new technologies.
• They contribute to the affordability of high-quality goods: The demand for high-quality, custom-made items has increased, and e-commerce and Outsourcing are becoming more crucial in delivering what customers want at a reasonable price by facilitating the creation and supply of high-quality products, e-business and outsourcing help to achieve the objective of excellence.
• They pave the way for effective after-sales service: Any company needs to meet the needs of its customers. Customers profit from e-commerce and outsourcing because they may receive quick and effective post-sale support.
• They speed up the business process: As consumer demands grow, it’s become critical to be able to do business from anywhere and at any time. E-commerce and outsourcing assist in speeding up the buying and selling process 24 hours a day, seven days a week.

The above-stated section of Important Questions Class 11 Business Studies Chapter 5 is a list of Important Questions covering the entire chapter.

Benefits of Solving Emerging Modes of Business Class 11 Important Questions

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Q.1 What does LPO stands for

A. Legal Process Outsourcing

B. Lower People Outsourcing

C. Legal Person Outsourcing

D. Lower Process Outsourcing

Marks: 1 Ans

Legal Process Outsourcing

Q.2 Karan wanted to establish a business after his studies. He decided to start a clothing business. However, after a discussion with his friends, some of them suggested to start a traditional business while some suggested to start online business. Can you help him in understanding the difference between the two types of business, so that Karan is able to choose the best mode of business

Marks: 5 Ans

Difference between traditional business and e-business

Q.3 The year 2020 saw a shift towards remote work instead of sitting and working in office. 16 million U.S. workers started working remotely in March. Most of the CFOs are planning to shift at least 5% of previously on-site employees to permanently remote positions after the quarantine.

This has opened the way for outsourcing as few companies have already understood that remote work and outsourcing are feasible options to keep their companies growing during the crisis or in times of pandemic. Give any two reasons why the companies are skeptical in outsourcing today also.

Outsourcing offers many benefits to the countries. But still the companies are sceptical in outsourcing today because of the following reasons: Confidentiality: Outsourcing involves sharing a lot of important information and knowledge. There is risk of outsourcing party not keeping the confidential information to itself. This risk all the more increases when a complete process or core activity of any business is outsourced. Sweat Shopping: For maximum benefits, outsorcer seeks to cut the costs. What is outsourced is the kind of components or work that does not much build the competency. Ethical concerns: To cut costs, outsources manufacturing to a developing country where they use child labour/women in the factories.

Q.4 Maya runs a successful retail store that sells designer clothes for women. The store building is taken on rent. Also, while checking sales, Maya observed that despite high sales, there is also high operating costs being incurred. She decided to change some policies and implemented the modes that can help her expand her business through online website.

(i) Identify and explain the mode of business that Maya decided to choose.

(ii) List down the resources required for successfully running an online business by Maya.

Marks: 6 Ans

(i) The mode of business that Maya decided to choose is e-business.

E-business is defined as the conduct business through use of internet and computer networks. Firms use secure and private networks for more effective and efficient management of their internal functions.

(ii) Resources required for successfully running an online business by Maya are:

• Appropriate computer hardware: Business needs to procure and install computers embedded with hardware that provide necessary speed and memory.
• Telecommunication system: An effective telecommunication system in the form of telephone lines, optic fiber cables and internet technology should be available with both- the business firm and the buyer.
• Qualified workforce: Business requires a well trained workforce having knowledge of working on internet and computer networks.
• System for receiving payment: Firm should make arrangement with banks and credit card agencies to facilitate electronic receipts and payments.

Q.5 Payment for online shopping can be done in a number of ways. Explain the ways briefly.

Payment for online transactions can made in the following ways:

i) Credit or Debit Cards : These are the most widely used medium for online transactions. Credit card allows its holder to make purchase on credit. Debit card allows its holder to make purchase through it to the extent of the amount lying in the corresponding account.

ii) Net-Banking : Most of the banks provide their customers with the facility of electronic transfer of funds over the net. A buyer may transfer the amount of the agreed price of the transaction to the account of an online vendor, post which the vendor would deliver the goods.

iii) Digital Cash : It is a form of electronic currency. Banks dealing in digital cash issue it after a customer deposits cash with the bank. Customers use digital funds to make purchases over the web and make payments.

iv) Cash-on Delivery : The payment of goods ordered online is made when the goods are physically delivered at the door of the customer. The payment is made in cash.

v) Cheque : Sometimes, an online vendor may ask a buyer to pay through cheque. The vendor may arrange for the pickup of the cheque from the customers end. Upon realisation, the delivery of goods may be made.

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Cbse class 11 business studies important questions, chapter 1 - business, trade and commerce.

Chapter 2 - Forms of Business Organisation

Chapter 3 - private, public and global enterprises, chapter 4 - business services, chapter 6 - social responsibilities of business and business ethics, chapter 7 - formation of a company, chapter 8 - sources of business finance, chapter 9 - small business, chapter 10 - internal trade, chapter 11 - international business, faqs (frequently asked questions), 1. what concepts are covered in important questions class 11 business studies chapter 5.

Important Questions Class 11 Business Studies Chapter 5 cover the concepts of the entire chapter- Emerging Modes of Business. But talking specifically, it discusses the meaning of e-business, the process of online buying and selling, distinguishing e-business from traditional business, benefits of switching to electronic mode, significant security concerns of e-business, need for business processing outsourcing, and so on.

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CBSE Class 11 Business Studies Revision Notes CHAPTER 5 Emerging Modes of Business class 11 Notes Business Studies

Meaning : In this age of internet, the world commerce has gradually started linking with it. This has brought a new concept of commerce called e-commerce/e-business. Now we are capable of reaching the users of Internet all over the world simply by opening a shop on the Internet. The Internet users can order for the goods, receive their delivery and make their payment while sitting at their home on the Internet.

Scope of e-Business

It can be understood by the view point of the parties involved and making transactions:

1. B2B Commerce : It is that business activity in which two firms or two business units make electronic transaction. For example- one can be producer firm and other a supplier firm.

2. B2C Commerce – Business to customer. In this one party is a firm and other party is a customer. On one hand a customer can seek information through Internet about products, place orders, get some items and make payments and on the other hand the firm can make a survey any time to know who is buying and can also know the satisfaction level of customers. In modern times, call centers can provide these information.

3. Intra-B Commerce Within business Commerce – Under it, the parties involved in the electronic transaction are the two departments of same business. For Example, through internet it is possible for the marketing department to interact constantly with the production department and get the customized goods made as per the requirement of customers.

4. C2C Commerce – Customer to Customer Commerce – Under it, both the parties involved in electronic transaction are customers. It is required for the buying and selling of those goods for which there are no established markets. For example-selling old car through internet.

5. C2B Commerce – C2B Commerce provides the Consumers with the freedom of shopping at will. Customer can make use of call centers to make toll free calls to make queries and lodge complaints.

6. B2E Commerce – Companies reporting to personnel recruitment, interview and selection and training etc. via B2E Commerce.

Benefits of e-Business

The major benefits of e-Business are as follows:

1. Worldwide reach- Internet gives businessmen an extended market. New customers come in contact with them. This results in increase in sales. 2. Elimination of Middlemen – Ever since the e-Business came into existence, the wholesalers and retailers have started disappearing. Now, most of the producers have started having direct contact with customers. As a result, the consumer get goods on less price. 3. Easy Distribution Process – Many types of information and services be received on computer through e-business. This has simplified the system of distribution and has also made it less costly. 4. Lower Investment required – In this, you don’t require any big showroom or huge investment. You need only computer and Internet. 5. Easy to launch new products – Any company can launch its new product in the market through the medium of E-Business. A complete information about the product is made available on Internet. In this way the consumer and other businessmen get information about the new product while sitting at home. 6. Movement towards a paperless Society – Use of internet has considerably reduced dependence on paper work.

Resources Required for Successful e-Business Implementation

The resources required for the e-Business are:

1. Computer system – The presence of computer system is the first requirement of e-Business. The computer can be linked with Internet by just pressing its keys. 2. Internet connection – Internet connection is very essential and now a days we can get this facility by sitting at home. 3. Preparing the web Page – web page has the greatest importance in the use of e-Business. It is also known as Home Page. Any product that is to be shown on Internet is displayed on web page. 4. Effective telecommunication system – e-business requires an effective telecommunication system in the form of telephone lines etc.

On Line Transactions

On line transaction means receiving information about goods, placing an order, Receiving delivery and making payment through medium of internet. Under this system, the sale purchase of every type of thing, information and service is possible.

Payment Mechanism

Payment for the purchases through online shopping may be done in following ways: 1. Cash on delivery (COD) – Cash payment can be made at the time of physical delivery of goods. 2. Net-banking transfer – The customer can make electronic transfer of funds(EFT) to account of online vendor over the internet. 3. Credit or Debit cards – The customer can make payment for online transaction through debit or credit card by giving the number and name of bank of card.

Security and Safety of e-Transactions

The following methods can be used to ensure security and safety of online transactions. 1. Confirming the details before the delivery of goods – The customer is required to furnish the details such as credit card no., card issuer and card validity online. 2. Anti VirusProgrammes – Installing and timely updating antivirus programmes provides protection to data files, folders and system from virus attacks. 3. Cyber crime cells – Govt. may setup special crime cells to look into the cases of hacking and take necessary action against the hackers.

Outsourcing or Business Process Outsourcing (BPO)

Many activities have to be performed for the successful conduct of business like productions, buying, selling, advertising etc. When the scale of business is small, the businessman used to perform these activities easily. However, with the enlargement of scale of business, this job has become tedious. Therefore, in order to overcome the difficulties connected with the performance of many activities and to get the benefit of specialization, these services are now obtained from outside the organization. This is called outsourcing of services or BPO.

Example: B.P.O.

If Reliance Industries Ltd. wants to advertise its ‘Vimal’ brand of clothing, it may appoint Anmol Advertising Co. to design, prepare and release advertisements on its behalf.

Need for BPO

BPO is essential for following reasons:

1. Obtaining Good Quality services – If a company attempts to perform all the activities itself, there is every possibility of quality of services being affected adversely. In order to avoid this difficulty, the need for obtaining services from outside is felt.

2. Avoiding Fixed Investment in Services – If a company attempts to get these services from within the organization itself, it has to establish different departments for this purpose which involves huge investment. Therefore, it appears justified to get these services from outside the organization at a little cost.

3. Smooth running of business – outsourcing of services is needed in order to run the business smoothly. The attention of businessman gets distracted from various small things and will be focused on the main activity.

Scope of BPO

In modern business many outside services are used. Out of these services, the following are the important ones:

1. Financial Services -These services means those outside services which help the company in some way or other in the management of finance.

2. Advertising services – Advertisement is very necessary for increasing sales. If this service is obtained from outside agency, it will cost less and the quality of advertisement will also be good.

3. Courier services – These services means delivering goods, documents. parcels from company to customers and vice-versa.

4. Customer support service – These services means delivering goods to customers and to give after sale services also. Generally, the manufacturers of TV, Fridge, AC etc. use these services.

KPO (Knowledge Process Outsourcing)

KPO refers to obtaining high end knowledge from outside the organization in order to run the business successfully and in cost effective manner. Unlike conventional BPO where the focus is on process expertise, in KPO the focus is on knowledge expertise.

Need of KPO

In today’s competitive environment focus is to concentrate on core specialization areas and outsources the rest of activities. Many companies have come to realise  that by outsourcing the non case activities not only costs are minimized and efficiency improved but the total business improves because the focus shifts tokey growth areas of business.

Features of KPO 1. It is the upward shift of BPO 2. It focuses on knowledge expertise instead of process expertise. 3. It provides all non case activities. 4 It has no pre-determined process to reach a conclusion. 5. It offers an alternative career path for the educated.

Scope of KPO/Services covered KPO 1. Research and Technical analysis. 2. Business and Technical analysis. 3. Business and Market research. 4. Animation and Design.

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Work, Energy and Power Class 11 Notes CBSE Physics Chapter 5 (Free PDF Download)

Revision Notes for CBSE Class 11 Physics Chapter 5 (Work, Energy and Power) - Free PDF Download

Work, Energy, and Power – a captivating chapter in CBSE Class 11 Physics! This chapter unravels the intricacies of some of the most fundamental concepts in physics that govern the motion and transformations of energy in our universe. From understanding the concept of work done by forces to exploring the different forms of energy and their interconversion, this chapter offers a comprehensive insight into the dynamics of energy in various physical systems. 

To aid your learning journey, we present you with these Class 11 Notes on Work, Energy, and Power – a free PDF download that condenses the key points, equations, and practical applications of the topic. With these notes at your disposal, you can embark on a fascinating voyage to comprehend the core principles that shape the behavior of physical systems and their energetic interplay. Let's dive in and unlock the secrets of this captivating realm!

Revision Notes for Class 11 Physics Chapter 5 - Work, Energy, and Power are available in Vedantu. These Revision Notes are written as per the latest Syllabus of NCERT. We hear the words 'work,' 'energy,' and 'power' all the time. A person carrying materials, a farmer cultivating, and a student studying for exams are all said to be performing their work. Work has a specific and definite meaning in Physics.

Topics Covered in Class 11 Physics Chapter 5 - Work, Energy, and Power  

Below are some of the key concepts discussed in this chapter.

The work-energy theorem

Kinetic energy

Work done by a variable force

The work-energy theorem for a variable force

The concept of potential energy

The conservation of mechanical energy

The potential energy of a spring

Law of conservation of energy

Download CBSE Class 11 Physics Revision Notes 2024-25 PDF

Also, check CBSE Class 11 Physics revision notes for other chapters:

Work, Energy and Power Chapter-Related Important Study Materials It is a curated compilation of relevant online resources that complement and expand upon the content covered in a specific chapter. Explore these links to access additional readings, explanatory videos, practice exercises, and other valuable materials that enhance your understanding of the chapter's subject matter.

Work, Energy and Power Class 11 Notes Physics - Basic Subjective Questions

Section – a (1 mark questions).

1. What is the unit of Power?

Ans. Watt (W)

2. Name the factors on which work is done depends.

Ans. Force, displacement and angle between force and displacement.

3. Work done by external forces is always equal to the gain in kinetic energy. Is it always true ? 

Ans. Yes. This is the universal work-energy theorem.

4. If energy is neither created nor destroyed, then from where do we get energy?

Ans. By transforming energy from one form to another.

5. A force $F=5\hat{i}+6\hat{j}-4\hat{k}$ acting on a body, produce a displacement $s=6\hat{i}+5\hat{k}$ Work done by the force.

Ans. $W=F\cdot s=\left ( 5\hat{j}+6\hat{j}-4\hat{k} \right )\left ( 6\hat{i}+5\hat{k} \right )$

=30-20=10 units

Section – B (2 Marks Questions)

6. List two conditions which need to be satisfied for the work to be done on an object?

(i) Force should be applied on the body.

(ii) Body should move in the direction of force.

7. An archer stretches a bow to release an arrow to hit the target at a distance of 10 m. Explain who does the work, in which form is the energy possessed by the bow and the arrow.

Ans. The archer does the work in pulling the bow string taut. The muscular energy of the archer arm a → potential energy of the taut string → kinetic energy of the arrow.

8. A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.

Ans. Work done = Force × displacement

= 15 × 10 × 1.5

9. A man of mass 60 kg runs up a flight of 30 steps in 40 s. If each step is 20 cm high, calculate his power. (take g = 10 m/s 2 )

Ans. Total height reached by $man=30\times \dfrac{20}{100}m=6m$

Power = work done/time = mgh / time 

$=\dfrac{60\times 10\times 6}{40}=90V$

10. An electric bulb of 100 W works for 4 hours a day. Calculate the units of energy consumed in 15 days.

Ans. Energy consumed = Power × Time

= 100 × 4 × 15

= 6 KWh = 6 units

PDF Summary - Class 11 Physics Work, Energy and Power Notes (Chapter 5)  

In Physics, work refers to ‘mechanical work’. Work is said to be done by a force on a body when the body is actually displaced through some distance in the direction of the applied force.

However, when there is no displacement in the direction of the applied force, there is no work done, i.e., work done is zero, when displacement of the body in the direction of the force is zero.

Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the body along the positive x-direction as shown in the following figure:

(Image will be updated soon)

If $\theta $ is the angle which F makes with the positive x-direction of the displacement, then the component of F in the direction of displacement is given by $F\cos \theta $. Since the work done by the force is the product of component of force in the direction of the displacement and the magnitude of the displacement, we can write:

$W=(F\cos \theta )s$

Now, when the displacement is in the direction of force applied, i.e., when $\theta ={{0}^{0}}$;

\[\Rightarrow W=\left( F\cos 0{}^\circ  \right)s=\vec{F}.\vec{s}\]

Clearly, work done by a force is the dot product of force and displacement.

In terms of rectangular components, $\vec{F}$ and $\vec{s}$ may be written as

\[\vec{F}=\hat{i}{{F}_{x}}+\hat{j}{{F}_{Y}}+\hat{k}{{F}_{Z}}\] and $\vec{s}=\hat{i}x+\hat{j}y+\hat{k}z$

$\Rightarrow W=\left( \hat{i}{{F}_{x}}+\hat{j}{{F}_{Y}}+\hat{k}{{F}_{Z}} \right).\left( \hat{i}x+\hat{j}y+\hat{k}z \right)$

$\Rightarrow W=x{{F}_{x}}+y{{F}_{y}}+z{{F}_{z}}$

Work is a scalar quantity, i.e., it has magnitude only and no direction. However, work done by a force can be positive, negative or zero.

2. DIMENSIONS AND UNITS OF WORK

As work $=$ force × distance;

$\Rightarrow W=({{M}^{1}}{{L}^{2}}{{T}^{-2}})\times L$

$\Rightarrow W=[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]$

This is the dimensional formula of work.

The units of work are of two kinds: a) Absolute units and b) Gravitational units

a) Absolute Units

Joule: It is the absolute unit of work in the SI system of units. Work done is said to be one joule, when a force of one newton actually moves a body through a distance of one meter in the direction of applied force.

$\Rightarrow 1joule=1newton\times 1metre\times \cos {{0}^{0}}=1N.m$

Erg: It is the absolute unit of work in the CGS system of units. Work done is said to be one erg, when a force of one dyne actually moves a body through a distance of one cm in the direction of applied force.

$\Rightarrow 1erg=1dyne\times 1cm\times \cos {{0}^{0}}=1dyne.cm$

b) Gravitational Units

These are also known as practical units of work.

Kilogram-meter (kg-m): It is the gravitational unit of work in the SI system of units. Work done is said to be one kg-m, when a force of 1kgf moves a body through a distance of 1m in the direction of the applied force.

$\Rightarrow 1kg-m=1kgf\times 1m\times \cos {{0}^{0}}=9.8N\times 1m=9.8joules$, i.e.,

$\Rightarrow 1kg-m=9.8J$

Gram-centimeter (g-cm): It is the gravitational unit of work in the CGS system of units. Work done is said to be one g-cm, when a force of 1gf

moves a body through a distance of 1cm in the direction of the applied force.

$\Rightarrow 1g-cm=1gf\times 1cm\times \cos {{0}^{0}}$

$\Rightarrow 1g-cm=980dyne\times 1cm\times 1$

$\Rightarrow 1g-m=980ergs$

3. NATURE OF WORK DONE

Although work done $\left( W=(F\cos \theta )s \right)$ is a scalar quantity, its value may be positive, negative, negative or even zero, as detailed below:

Positive Work is said to be done on a body when $\theta $ is acute ($<{{90}^{0}}$). Clearly, $\text{cos}\theta $ turns out to be positive and hence, the work done is positive.

For example, when a body falls freely under the action of gravity,$\theta ={{0}^{0}};\cos \theta =\cos {{0}^{0}}=+1$. Clearly, work done by gravity on a body falling freely is positive.

Negative Work is said to be done on a body when $\theta $ is obtuse ($>{{90}^{0}}$). Clearly, $\text{cos}\theta $  is negative and hence, the work done is negative.

For example, when a body is thrown up, its motion is opposed by gravity. The angle $\theta $ between gravitational force and the displacement is ${{180}^{0}}$. Since $\cos \theta =\cos {{180}^{0}}=-1$; work done by gravity on a body moving upwards is negative.

(image will be updated soon)

Zero Work is said to be done on a body when force applied on it or the displacement caused or both of them are zero. Here, when angle $\theta $ between force and displacement is ${{90}^{0}}$; $\cos \theta =\cos {{90}^{0}}=0$ and hence, the work done is zero.

For example, when we push hard against a wall, the force we exert on the wall does no work because displacement is zero in this case. However, in this process, our muscles are contracting and relaxing alternately and internal energy is being used up. This is why we do get tired.

4. WORK DONE BY A VARIABLE FORCE

Graphical Method:

A constant force is rare. It is the variable force which is encountered more commonly. 

To evaluate the work done by a variable force, let us consider a force acting along a fixed direction, say x–axis, but having a variable magnitude.

We have to compute work done in moving the body from A to B under the action of this variable force. 

To facilitate this, we assume that the entire displacement from A to B is made up of a large number of infinitesimal displacements.

One such displacement shown in the following figure from P to Q.

Since the displacement $PQ=dx$ is infinitesimally small, we consider that all along this displacement, force is constant in magnitude as well in the same direction.

Now, a small amount of work done in moving the body from P to Q is given by,

$dW=F\times dx=(PS)(PQ)=area\text{ }of\text{ }strip\text{ }PQRS$

Therefore, the total work done in moving the body from A to B is given by

$\Rightarrow W=\sum{dW}$

$\Rightarrow W=\sum{F\times dx}$

Here, when the displacement is allowed to approach zero, then the number of terms in the sum increases without a limit. And the sum approaches a definite value equal to the area under the curve CD.

Thus, we may rewrite that 

$\Rightarrow W=\underset{dx\to x}{\mathop{\lim }}\,\sum{F(dx)}$

Using integral calculus, we may write it as

$\Rightarrow W={}_{{{X}_{A}}}^{{{X}_{B}}}\int{A(dx)}$ 

${{x}_{A}}={{O}_{A}}$ and ${{x}_{B}}=OB$

$\Rightarrow W={}_{{{X}_{A}}}^{{{X}_{B}}}\int{area\text{ }of\text{ }strip\text{ }PQRS}$

Which is nothing but the total area under the curve between F and x-axis from $x={{x}_{A\text{ }}}\text{ }to\text{  }x={{x}_{B}}$.

$\Rightarrow W=Area\text{ }of\text{ }ABCDA$

Clearly, the work done by a variable force is numerically equal to the area under the force curve and the displacement axis.

Mathematical Treatment (of work done by a variable force)

Suppose we have to evaluate the work done in moving a body from a point A (${{S}_{A}}$) to point B (${{S}_{B}}$) under the action of a varying force as shown in the following figure. Here, ${{S}_{A}}$ and ${{S}_{B}}$ are the distance of the points A and B with respect to some reference point.

At any stage, let the body be at P, where force on the body is $\vec{F}$. 

Under the action of this force, let the body undergo an infinitesimally small displacement $d\vec{s}$

During such a small displacement, if we assume that the force remains constant, then small amount of work done in moving the body from P to Q is

$dW=\vec{F}.d\vec{s}$

Now, when the displacement is zero, the total work done in moving the body from A to B can be obtained by integrating the above expression between ${{S}_{A}}$and ${{S}_{B}}$ as follows:

\[\Rightarrow W={}_{{{S}_{A}}}^{{{S}_{B}}}\int{\vec{F}.d\vec{s}}\] 

5. CONSERVATIVE & NON­CONSERVATIVE FORCES

Conservative Force

A force is said to be conservative when the work done by or against the force in moving a body is dependent only on the initial and final positions of the body, and not on the nature of path followed between the initial and the final positions.

This suggests that the work done by or against a conservative force in moving a body over any path between fixed initial and final positions would be the same.

For instance, gravitational force is a conservative force.

Properties of Conservative Forces :

Work done by or against a conservative force in moving a body from one position to the other depends only on the initial position and final position of the body.

Work done by or against a conservative force does not depend upon the nature of the path followed by the body in going from initial position to the final position.

Work done by or against a conservative force in moving a body through any round trip (i.e., closed path, where final position coincides with the initial position of the body) is always zero.

Non-conservative Forces

A force is said to be non-conservative when the work done by or against the force in moving a body from one position to another, is dependent on the path followed between these two positions.

For instance, frictional forces are non-conservative forces.

Power of a person or machine refers to the time rate at which work is done by it.

Mathematically,

Power $=$ Rate of doing work $=$ $\frac{work\text{ }done}{time\text{ }taken}$

Thus, power of a body measures how fast it can do the work.

$\Rightarrow P=\frac{dW}{dt}$

Now, it is known that $\text{dW=\vec{F}}\text{.d\vec{s}}$;

$\Rightarrow P=\frac{\vec{F}.d\vec{s}}{dt}$

But $\frac{d\vec{s}}{dt}=\vec{v}$, which is the instantaneous velocity.

$\Rightarrow P=\vec{F}.\vec{v}$

Dimensions of power is given by

$P=\frac{W}{t}=\frac{{{M}^{1}}{{L}^{2}}{{T}^{-}}}{{{T}^{1}}}=[{{M}^{1}}{{L}^{2}}{{T}^{-3}}]$

Units of power

The absolute unit of power in SI system of units is watt, which is denoted by $W$.

$\Rightarrow P=\frac{W}{t}$

$\Rightarrow 1watt=\frac{1joule}{1\text{ }\sec }\Rightarrow 1W=1J{{s}^{-1}}$

Clearly, power of a body is said to be one watt, when it can do one joule of work in one second. A bigger unit if power is horsepower (hp), given by

Energy of a body refers to the capacity or ability of the body to do work.

8. KINETIC ENERGY

The kinetic energy of a body refers to the energy possessed by the body by virtue of its motion.

Here are some examples:

A bullet fired from a gun can pierce through a target on account of kinetic energy of the bullet.

Wind mills work on the kinetic energy of air. For instance, sailing ships use the kinetic energy of wind.

Water mills work on the kinetic energy of water. For instance, fast flowing streams are utilized to grind corn.

A nail is driven into a wooden block on account of kinetic energy of the hammer striking the nail.

Formula for Kinetic Energy

Kinetic Energy of a body can be obtained either from

the amount of work done in stopping the moving body, or from

the amount of work done in giving the present velocity to the body from the state of rest.

Let us first consider the second method:

Suppose that, 

m$=$ mass of a body at rest (i.e., u$=$0).

F$=$Force applied on the body

a$=$acceleration produced in the body in the direction of force applied.

v$=$velocity acquired by the body in moving through a distance ‘s’, as shown in the following diagram.

Now, consider the equation of motion: $v-u=2as$;

$\Rightarrow {{v}^{2}}-0=2as$

$\Rightarrow a=\frac{{{v}^{2}}}{2s}$

It is known that 

$\Rightarrow F=m\left( \frac{{{v}^{2}}}{2s} \right)$

Clearly, work done on the body, (W $=$ Force × distance)

$\Rightarrow W=m\frac{{{v}^{2}}}{2s}\times s$

$\Rightarrow W=\frac{1}{2}m{{v}^{2}}$

This work done on the body is a measure of kinetic energy (K.E.) acquired by the body,

$\Rightarrow K.E\text{ }Of\text{ }the\text{ }body=W=\frac{1}{2}m{{v}^{2}}$

Alternative Method

The formula for kinetic energy of a body can also be obtained by the method of calculus as follows:

Let m$=$mass of a body, which is initially at rest (i.e., u$=$0)

$\vec{F}$$=$Force applied on the body,

$d\vec{s}$$=$ small displacement produced in the body in the direction of the force applied.

A small amount of work done by the force is given by,

$dW=\vec{F}.d\vec{s}=Fds\cos {{0}^{0}}=Fds$

If ‘a’ is the acceleration produced by the force, then from

$F=ma=m\frac{dv}{dt}$ and from 

$dW=\left( m\frac{dv}{dt} \right)ds=m\left( \frac{ds}{dt} \right)dv$;

$\Rightarrow dW=mvdv\text{     }\left( \because \frac{ds}{dt}=v \right)$

Thus, the total work done by the force in increasing the velocity of the body from zero to v is given by

$W=\int\limits_{0}^{v}{mvdv}=\frac{1}{2}m{{v}^{2}}$

Thus, kinetic energy of a body is half the product of mass of the body and square of velocity of the body.

9. RELATION BETWEEN KINETIC ENERGY AND LINEAR MOMENTUM

If m is the mass of a body and v is the velocity of the body;

Linear momentum of the body is given by \[p=mv\] and K.E. of the body is given by $KE=\frac{1}{2}m{{v}^{2}}=\frac{1}{2m}({{m}^{2}}v)$

$\Rightarrow KE=\frac{p}{2m}$

This is an important relation. It shows that a body cannot have kinetic energy without having linear momentum. The reverse is also true.

Further, if linear momentum (p) is constant, then,

$KE \propto \frac{1}{m}$

This is shown in figure (a).

On the other hand, if kinetic energy (KE) is constant, then,

${{p}^{2}}\propto m\text{ }or\text{ }p\propto \sqrt{m}$

This is shown in figure (b).

Also, if mass (m) is constant, the,

${{p}^{2}}\propto KE\text{ }or\text{ }p\propto \sqrt{KE}$

This is shown in figure (c).

10. WORK ENERGY THEOREM OR WORK ENERGY PRINCIPLE

According to this principle, work done by net force in displacing a body is the same as the change in kinetic energy of the body.

Thus, when a force does some work on a body, the kinetic energy of the body increases by the same amount. Conversely, when an opposing (retarding) force is applied on a body, its kinetic energy decreases. The decrease in kinetic energy of the body is equal to the work done by the body against the retarding force. Thus, according to work energy principle, work and kinetic energy are equivalent quantities.

Proof: To prove the work-energy theorem, we confine ourselves to motion in one dimension.

Suppose that m$=$mass of a body, u$=$initial velocity of the body, F$=$force applied on the body along it direction of motion, a$=$acceleration produced in the body, v$=$final velocity of the body after t second.

Small amount of work done by the applied force on the body is given by $dW=F(ds)$, when ds is the small distance moved by the body in the direction of the force applied.

$F=ma=m\left( \frac{dv}{dt} \right)ds=m\left( \frac{ds}{dt} \right)dv=mvdv\left( \therefore \frac{\text{ds}}{\text{dt}}=v \right)$

Total work done by the applied force on the body in increasing its velocity from u to v is given by

\[W=\int\limits_{u}^{v}{mvdv}=m\left[ \frac{{{v}^{2}}}{2} \right]_{u}^{v}\]

$\Rightarrow W=\frac{1}{2}m(v-u)=\frac{1}{2}mv-\frac{1}{2}mu$

But $\frac{1}{2}m{{v}^{2}}={{K}_{f}}=final\text{ }KE\text{ }of\text{ }the\text{ }body\text{ }and\text{ }\frac{1}{2}m{{u}^{2}}={{K}_{i}}=initial\text{ }KE\text{ }of\text{ }the\text{ }body$

$\Rightarrow W={{K}_{f}}-{{K}_{i}}=increases\text{ }in\text{ }KE\text{ }of\text{ }body$

i.e., work done on the body is equal to the increase in KE of the body.

11. POTENTIAL ENERGY

The potential energy of a body refers to the energy possessed by the body by virtue of its position or configuration in some field.

Thus, potential energy is the energy that can be associated with the configuration (or arrangement) of a system of objects that exert forces on one another. Obviously, if configuration of the system changes, then its potential energy changes.

Two important types of potential energy are:

Gravitational potential energy

Elastic potential energy.

11.1 Gravitational Potential Energy

Gravitational potential energy of a body refers to the energy possessed by the body by virtue of its position above the surface of the earth.

To calculate gravitational potential energy, suppose

m$=$mass of a body

g$=$acceleration due to gravity on the surface of earth.

h$=$height through which the body is raised, as shown in the following figure.

If we assume that height ‘h’ is not too large and the value of ‘g’ is practically constant over this height, then the force applied just to overcome gravitational attraction is given by,

As the distance moved is in the direction of the force applied, work can be expressed as:

Work done$=$force × distance

$\Rightarrow W=F\times h=mgh$

Notice that we have taken the upward direction to be positive. Therefore, work done by applied force$=+mgh$. However, work done by gravitational force$=-mgh$.

This work gets stored as potential energy. The gravitational potential energy of a body, as a function of height (h) is denoted by V(h), and it is negative of work done by the gravitational force in raising the body to that height.$\Rightarrow Gravitational\text{ }PE=V(h)=mgh$

11.2 Potential Energy of a Spring

Potential energy of a spring refers to the energy associated with the state of compression or expansion of an elastic spring.

To compute it, consider an elastic spring OA of negligible mass. The end O of the spring is fixed to a rigid support and a body of mass ‘m’ is attached to the free end A. Let the spring be oriented along the x–axis and the body of mass ‘m’ lie on a perfectly frictionless horizontal table.

The position of the body A, when spring is unstretched, is chosen as the origin. Now, when the spring is compressed or elongated, it tends to recover to its original length, on account of elasticity. The force trying to bring the spring back to its original configuration is termed restoring force or spring force.

For a small stretch or compression, spring obeys Hooke's law, i.e., for a spring,

Restoring Force $\propto $ stretch or compression

$\Rightarrow -F\propto x\text{ }or\text{ }-F=kx$

where k is a constant of the spring called the spring constant.

It is established that for a spring, $k\propto \frac{1}{l}$. i.e., smaller the length of the spring, greater would be the force constant and vice-versa.

The negative sign in the equation indicates that the restoring force is always directed towards the equilibrium position.

Now, consider that the body be displaced further through an infinitesimally small distance dx, against the restoring force.

A small amount of work done in increasing the length of the spring by dx is given by,

$dW=-Fdx=kxdx$

Thus, the total work done in giving displacement x to the body can be obtained by integrating from $x=0$ to $x=x$, i.e.,

$W=\int\limits_{x=0}^{x=x}{kxdx}=\frac{1}{2}k{{x}^{2}}$

This work done is stored in the spring at the point B.

$\Rightarrow PE\text{ }at\text{ }B=W=\frac{1}{2}k{{x}^{2}}$

The variation of potential energy with distance x is as shown in the following figure.

12. MECHANICAL ENERGY AND ITS CONSERVATION

The mechanical energy (E) of a body refers to the sum of kinetic energy (K) and potential energy (V) of the body

i.e., $E=K+V$

Obviously, mechanical energy of a body is a scalar quantity measured in joules.

We can show that the total mechanical energy of a system is conserved if the force doing work on the system is conservative.

This is known as the principle of conservation of total mechanical energy.

For simplicity, we assume the motion to be one dimensional only. Suppose a body undergoes a small displacement ‘x’ under the action of a conservative force F. According to the work energy theorem, change in kinetic energy is equal to the work done.

$\Rightarrow \Delta K=F(x)\Delta x$

Now, as the force is conservative, the potential energy function V(x) is defined as

\[-\Delta V=F(x)\Delta x\text{ }or\text{ }\Delta V=-F(x)\Delta x\]

Adding both the above expressions, we get,

$\Rightarrow \Delta K+\Delta V=0\text{ }or\text{ }\Delta (K+V)=0$,

which means that

$(K+V)=E=constant$

12.1 Illustration of the Law of Conservation of Mechanical Energy

To illustrate the law further, let us evaluate kinetic energy, potential energy, and total energy of a body falling freely under gravity.

Let ‘m’ be the mass of the body held at A, at a height h above the ground, as shown in the following figure.

As the body is at rest at A, therefore,

KE of the body is zero.

PE of the body is equal to mg, where g is acceleration due to gravity at A.

$\Rightarrow TE\text{ }of\text{ }the\text{ }body=KE+PE=0+mgh$

$\Rightarrow {{E}_{A}}=mgh$….(1)

Now, let the body be allowed to fall freely under gravity, when it strikes the ground at C with a velocity ‘v’.

From ${{v}^{2}}-{{u}^{2}}=2as$;

$\Rightarrow {{v}^{2}}-0=2(g)h$

$\Rightarrow {{v}^{2}}=2gh$….(2)

Therefore, at C;

KE of the body$=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m(2gh)=mgh$

PE of the body\[=mgh=mg\left( 0 \right)=0\]

Total energy of the body is given by,

$TE={{E}_{C}}=mgh+0=mgh$.... (3)

Now, in free fall, let the body cross any point B with a velocity ${{v}_{1}}$, where AB is equal to ‘x’. Thus, from ${{v}^{2}}-{{u}^{2}}=2as$;

$\Rightarrow v_{1}^{2}-0=2(g)x$…. (4)

$\Rightarrow v_{1}^{2}=2gx$

Clearly, at B;

KE of the body$=\frac{1}{2}mv_{1}^{2}=\frac{1}{2}m(2gx)=mgx$

Height of the body at B above the ground\[=CB=\left( hx \right)\]

PE of the body at B\[=mg\left( hx \right)\]

Total energy of the body at B\[=KE+PE\]

$\Rightarrow {{E}_{B}}=mgx+mg(h-x)=mgx+mgh-mgx$

$\Rightarrow {{E}_{B}}=mgh$.... (5)

Clearly, from (1), (3), and (5); we find that

${{E}_{A}}={{E}_{C}}={{E}_{B}}=mgh$

13. DIFFERENT FORMS OF ENERGY

We have learnt some details of potential energy and kinetic energy. It should be understood that these are not the only two forms of energy. Energy may manifest itself in several other forms. Some of the examples are:

Heat Energy

It is the energy possessed by a body by virtue of random motion of the molecules of the body.

Heat is also associated with the force of friction. When a block of mass ‘m’ sliding on a rough horizontal surface with speed ‘v’, stops over a distance ‘x’, work done by the force of kinetic friction ‘f’ over a distance ‘x’ is given by $-f(x)$. By the work energy theorem, $\frac{1}{2}m{{v}^{2}}=f(x)$ .We often say that kinetic energy of the block is lost due to frictional force. However, when we examine the block and the horizontal surface carefully, we detect a slight increase in their temperatures. Thus, work done by friction is not lost, but is transferred as heat energy of the system.

Internal Energy

It is the total energy possessed by the body by virtue of particular configuration of its molecules and also their random motion. Thus, internal energy of a body is the sum of potential energy and kinetic energy of the molecules of the body.

Electrical Energy

The flow of electric current causes bulbs to glow, fans to rotate and bells to ring. A definite amount of work has to be done in moving the free charge carriers in a particular direction through all the electrical appliances.

Chemical Energy

Chemical energy arises from the fact that the molecules participating in the chemical reaction have different binding energies. A chemical reaction is basically a rearrangement of atoms. For example, coal consists of carbon and a kilogram of it. When burnt, it releases $3\times {{10}^{7}}J$ of energy.

Nuclear Energy

It is the energy obtainable from an atomic nucleus. Two distinct modes of obtaining nuclear energy are nuclear fission nuclear fusion.

Nuclear fission involves splitting of a heavy nucleus into two or more lighter nuclei, whereas nuclear fusion involves fusing of two or more lighter nuclei to form a heavy nucleus.

14. MASS ENERGY EQUIVALENCE

Einstein made an incredible discovery that energy can be transformed into mass and mass can be transformed into energy. To put it precisely, one energy can be obtained at the cost of the other energy.

The mass energy equivalence relation as put forth by Einstein is

$E=m{{c}^{2}}$

m is the mass that disappears; 

E is the energy that appears;

C is the velocity of light in vacuum.

Mass and energy are not conserved separately, but are conserved as a single entity called ‘mass-energy’.

15. THE PRINCIPLE OF CONSERVATION OF ENERGY

If we account for all forms of energy, the total energy of an isolated system does not change.

The principle of conservation of energy cannot be proved as such. However, no violation of this principle has ever been observed.

16. WORK DONE BY A VARIABLE FORCE

When the force is an arbitrary function of position, we require the techniques of calculus to determine the work done by it. The figure shows F(x) as some function of the position x. To calculate work done by F from A to B, we find the area under the graph from ${{X}_{A}}\text{ }to\text{ }{{X}_{B}}$.

Thus, the work done by a force F(x) from an initial point A to final point B is given by,

${{W}_{A\to B}}=\int\limits_{{{X}_{A}}}^{{{X}_{B}}}{{{F}_{X}}dx}$

17. CONSERVATIVE & NON­CONSERVATIVE FORCES

17.1 Conservative Forces

A force is conservative if the net work done against the force in moving a mass between two points depends only on the location of two points and not on the path followed.

17.2 Non-Conservative Forces

Those forces which do not satisfy the above-mentioned criteria are termed non-conservative forces. Friction and viscous forces are the most common examples of non-conservative forces.

17.3 Conservative Forces and Potential Energy

For every conservative force, there is a corresponding potential energy function. In each case, the potential energy expression is dependent only on position. For every conservative force ${{F}_{X}}$, that depends only on the position ‘x’, there is an associated potential energy function U(x). When conservative force does positive work, the potential energy of the system decreases. Work done by conservative force is given as:

$F(x)\Delta x=-\Delta U$

$\Rightarrow F(x)=\frac{-\Delta U}{\Delta x}$

which, in the limit, becomes, 

$\Rightarrow F(x)=-\frac{dU}{dx}$

Integrating both sides for a displacement from\[x=a\text{ }to\text{ }x=b\], we have,

\[\Rightarrow {{U}_{b}}-{{U}_{a}}=-\int\limits_{b}^{a}{F(x)dx}\]

18. DYNAMICS OF CIRCULAR MOTION

18.1 Force on the Particle

In uniform circular motion, acceleration is of magnitude $\frac{{{v}^{2}}}{r}$ and is directed towards the center. Thus, a force of magnitude $\frac{m{{v}^{2}}}{r}$ and directed towards the center is needed to keep a particle in circular motion. 

This force (acting toward center) is called the centripetal force. Centripetal force is not an extra force on a body. Whatever force is responsible for circular motion becomes the centripetal force.

Examples  

When a satellite revolves around the earth, the gravitational attraction of earth becomes the centripetal force for the circular motion of that satellite; 

When an electron revolves around the nucleus in an atom, the electrostatic attraction of the nucleus becomes the centripetal force for the electron’s circular motion. 

In case of a conical pendulum, \[Tsin\theta \](component of tension) becomes the centripetal force.

18.2 Main steps for analyzing forces

Consider an axis along the radius of circle (i.e., in the direction of acceleration) and another axis perpendicular to the radius. Resolve all the forces into components.

Net force along perpendicular axis is equal to zero.

Net force along radial axis (towards center)$=\frac{m{{v}^{2}}}{r}=m{{\omega }^{2}}r$.

18.3 Main Steps for Analyzing Forces in Non–Uniform Circular Motion

Once we resolve all the forces along tangential and radial axes;

Net tangential force $={{F}_{t}}=m{{a}_{t}}$

Net radial force = $={{F}_{r}}=m{{a}_{r}}=\frac{m{{v}^{2}}}{r}$

Example of non-uniform circular motion  

The motion of particles in a vertical circle. If a particle is revolved in a vertical circle with the help of a string, the forces are: tension (T) towards center and weight (mg). 

In case of a particle moving along the outside surface of a circular track (or sphere), the forces are: normal reaction (N) away from the center and weight (mg).

18.4 Conical Pendulum

A small block of mass ‘m’ is rotated in a horizontal circle with the help of a string of length ‘l’ connected to ‘m’. The other end of the string is fixed to a point O vertically above the center of the circle so that the string is always inclined with the vertical at an angle. Such an arrangement is referred to as a conical pendulum as shown in the following diagram.

With respect to the force diagram of the block;

Along the vertical:

$T\cos \theta =mg$…(1)

Net force towards center,

\[Tsin~\theta =ma\]

$\Rightarrow \text{Tsin}\theta \text{=m}{{\omega }^{2}}r$…(2)

From (1) and (2), we have,

\[{{\omega }^{2}}=\frac{g\tan \theta }{r}=\frac{g\tan \theta }{l\sin \theta }=\frac{g}{l\cos \theta }\]

$\Rightarrow Time\text{ }period=T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{l\cos \theta }{g}}$

If ‘h’ is the height of point O above the center of the circle, then time period is equal to $2\pi \sqrt{\frac{h}{g}}$.

For a conical pendulum, 

${{\omega }^{2}}l\cos \theta =g$

$\Rightarrow \omega >\sqrt{\frac{g}{l}}$ (Because \[cos~\theta <l\])

18.5 Motion in a Vertical Circle

For a mass ‘m’ tied to a string of length ‘l’ and rotated in a vertical circle with center at the other end of the string, let is determine:

(a) the minimum velocity of the mass at the top of the circle so that it is able to complete the circle.

(b) the minimum velocity at the bottom of the circle.

At all positions, there are two forces acting on the mass: its own weight and the tension in the string.

Let the radius of the circle be equal to one unit.

(a) At the Top 

Let ${{v}_{t}}=$velocity at the top;

Net force towards center$=\frac{mv_{t}^{2}}{l}$

$T+mg=\frac{mv_{t}^{2}}{l}\Rightarrow T=\frac{mv_{t}^{2}}{l}-mg$

For the movement in the circle, the string must remain tight i.e., the tension should be positive at all positions.

As the tension is minimum at the top ${{\text{T}}_{top}}\ge 0$;

$\Rightarrow \frac{mv_{t}^{2}}{l}-mg\ge 0\Rightarrow {{v}_{t}}\ge \sqrt{{{l}_{g}}}$

$\Rightarrow $ minimum or critical velocity at the top = $=\sqrt{{{l}_{g}}}$

(b) At the Bottom

Let ${{v}_{b}}$ be the velocity at the bottom. As the particle goes up, its kinetic energy decreases and gravitational potential energy increases.

$\Rightarrow $loss in KE is equal to gain in GPE

$\Rightarrow \frac{1}{2}mv_{b}^{2}-\frac{1}{2}mv_{1}^{2}=mg(2l)$

$\Rightarrow v_{b}^{2}=v_{t}^{2}+4gl$

$\Rightarrow {{({{v}_{b}})}_{\min }}=\sqrt{{{(v_{t}^{2})}_{\min }}+4gl}=\sqrt{5gl}$

When a particle moves in a vertical circle, its speed reduces as it goes up and its speed rises as it comes down. Clearly, it is an example of non-uniform circular motion.

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CBSE Class 11 Physics Notes Chapter 5 Work, Power and Energy

In this context, we are going to discuss the list of content on what is work, power and energy. When we talk about Physics, the chapter of work, power, and energy is one of the most important chapters which involves concepts of mechanics.

The utmost collective illustrations that aid a concept of work, power and energy are a car in motion, bracing heavy objects, walking upstairs, an aeroplane flying and so on.

Some concepts regarding Chapter Work, Power, and Energy are precisely described in physics. So, these concepts can help you to do some measurements. Also, these perceptions can be utilized to describe and calculate the motion and its behaviour among multiple figures.

Chapter 5 Physics Class 11 Notes

What do you mean by Work?

Work can be defined as the amount of energy that transfers when a body is moved by an outside (external) force propagated in the displacement’s direction.

What do you mean by Power?

The definition of power can be explained as the rate at which the work is accomplished. Mathematically, Power = Work/time

What do you mean by Energy?

The definition of energy can be explained as the capability of doing work.

Energy has many forms. The most popular forms of energy are kinetic, thermal, potential, electrical, chemical, nuclear, etc.

The SI unit of work and energy is the same.

There is a list of physics of class 11 chapter 5 work, energy, and power.

Work Energy and Power Class 11 Notes (Table will be updated soon)

Notes of work energy and power class 11.

Here are some important questions under Class 11 Chapter 5 Physics Notes.

Q1. The aircraft casing burns up by friction. Find the energy obtained required for the burning of the casing.

Ans: The mass of the rocket reduces at the time of the burning of the casing due to the friction.

No reaction is beyond the law of conservation of energy. 

So, E Total = Potential energy + Kinetic energy = mgh + ½ mv 2

It is noticed that a drop in total energy happens due to the reduction in the mass of the aircraft. That is the reason for which energy is required for the burning of the casing which is obtained from the rocket.

Q2. If a ball of mass 5 kg is placed on a higher ground of 3 meters, find the potential energy stored in that body.

Ans: Given, m = 5 kg

We know that g = 9.81 m/s -2

So, Potential energy = m * g * h = 5 * 3 * 9.81 = 147.15 J

Work Done by a Variable Force and Conservative and Non-Conservative Forces

These two sections in Physics Class 11 Chapter 5 Notes explain about the work done by variable forces and details regarding conservative and non-conservative forces. 

Power And Energy

In this section of the Notes of Physics Class 11 Chapter 5 the concepts of power and energy along with their measurable units, expressions, etc.

Kinetic Energy, Relation Between Kinetic Energy and Linear Momentum

In this segment, students will get to know about different real-life applications of kinetic energy, expression to determine K.E of a body and its relation with linear momentum.

Work Energy Theorem or Work Energy Principle

As per the work energy principle, the amount of work done to move a body is equivalent to kinetic energy change. Precise analysis of the theory is laid out in this section.

Potential Energy

Another crucial topic is potential energy. Go through Physics Chapter 5 Class 11 Notes and be familiar with the different types of potential energy – gravitational and elastic potential energy.

Mechanical Energy and its Conservation

What is mechanical energy? It is nothing but the sum of the kinetic and potential energy of a body. Comprehensive elucidation of the same is provided in class 11 Chapter 5 Physics Notes to clear your concepts.

Different Energy Forms, Mass Energy Equivalence and Principle of Conservation of Energy

This section discusses different energy forms available like heat energy, internal energy, etc. furthermore, you will also get to know the mass energy equivalence expression stated by Einstein and conservation of energy principle.

Work Done by a Variable Force and Dynamics of Circular Motion

The last portion of the notes of Physics Class 11 Chapter 5 explain topics like work done by a force from point A to B, and forces related to uniform and non-uniform circular motion.

Proper understanding of the concepts is necessary to write precise answers and solve numerical problems. Hence, along with the text, refer to Class 11 Chapter 5 Physics notes offered by Vedantu.

Important Questions from Work, Energy, and Power (Short, Long, and Practice Questions)

Short answer type questions.

1.  A spring is kept compressed by pressing its ends together lightly. It is then placed in strong acid and released. What happens to its stored potential energy?

2. Why are the clock pendulums made of invar, a material of low value of the coefficient of linear expansion?

3. How would a thermometer be different if glass expanded more with increasing temperature than mercury?

Long Answer Type Questions

1. An object of mass 0.4kg moving with a velocity of 4m/s collides with another object of mass 0.6kg moving in the same direction with a velocity of 2m/s. If the collision is perfectly inelastic, what is the loss of K.E. due to impact?

2. A ball is dropped on the floor from a height of 2cm. After the collision, it rises up to a height of 1.5m. Assuming that 40% of mechanical energy lost goes to thermal energy into the ball. Calculate the rise in temperature of the ball in the collision. The specific heat capacity of the ball is 800J/k. Take g = 10m/s 2 .

3. If the volume of a block of metal changes by 0.12% when it is heated to 200C. What is the coefficient of linear expansion of the metal?

Practice Questions

1. If one Mole of a monatomic gas is mixed with 3 moles of a diatomic gas. What is the molecular-specific heat of the mixture at constant volume?

2. A stone of mass 5 kg falls from the top of a cliff 30 m high and buries itself one metre deep into the sand. Find the average resistance offered and the time taken to penetrate into the sand.

3. A pump on the ground floor of a building can pump up water to fill a tank of volume 30m 3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?

Why Choose Vedantu for CBSE Class 11 Physics Notes?

Vedantu provides a definitive study tool for students in the form of concepts of chapters along with the arranged question sets as per CBSE guidelines.

The chapters of Physics and its respective questions are based on the CBSE board syllabus. The notes also come with numerous concepts and practice papers.

Scholars can have the best education along with practice sets and mock tests for fluency in the specific chapter. They can learn time-management skills by practising Vedantu’s curated questions.

Key Features of Revision Notes for Class 11 Physics Chapter 5 - Work, Energy, and Power

Revision Notes are curated in order to help students in quickly finding important concepts from Work, Energy, and Power.

All concepts are explained in a detailed manner.

Revision Notes are clear and easy to understand as they are prepared by subject experts to match the syllabus.

These Revision Notes on Work, Energy, and Power help students in developing strong conceptual foundations for students, which is important in the final stages of preparation for board and competitive exams.

These Important Questions are available in PDF format and can be downloaded for free.

The CBSE Class 11 Notes on Work, Energy, and Power offer a comprehensive and concise resource for understanding the fundamental concepts that govern the dynamics of energy in the physical world. The chapter explores the concept of work done, the various forms of energy, and their interconversion, providing students with a solid foundation in this essential aspect of physics. With these free PDF notes at their disposal, students can reinforce their understanding, revise key points, and practice important equations. By mastering the principles of work, energy, and power, students can confidently approach complex physics problems and delve deeper into the fascinating world of energy transformations and their practical applications.

FAQs on Work, Energy and Power Class 11 Notes CBSE Physics Chapter 5 (Free PDF Download)

1. Is it Possible to Create Infinite Energy?

No, it is not possible. The universe does not have any infinities. In this universe, everything is finite in mass, size, time and energy. Infinity means something big which can’t be counted, which is impossible.

2. Calculate the Kinetic Energy Attained by a Football of Mass 0.46 kg Travelling at a Speed of 60 m/s.

We know that m = 0.46 kg

Velocity, v = 60 m/s

So, Kinetic energy = ½ mv 2 = ½ * 0.46 * 60 = 13.8 J

3. Mention Some Important Features of Vedantu for CBSE Board Exams.

Vedantu has taken part in so many educational activities. Vedantu has always focused on quality studies for Physics also.

The responsiveness, along with thorough question and answer practice papers, is very helpful to the students as per the CBSE board exam point of view.

4. What do you Mean by Internal Forces? Give Examples.

Internal forces are the types of forces that are present inside the body and act upon it internally. Examples of internal forces are the gravity forces, magnetic force, electrical force and spring force. We can’t see the gravitational force, but it acts upon every object that stays on earth. The concept is the same for all the examples given above.

5. Can you please provide a detailed stepwise study plan to ace Class 11 Physics, Chapter 5 - Work, Energy and Power?

The first step to ace Class 11 Physics, Chapter 5 - Work, Energy and Power is to thoroughly read the chapter from the NCERT textbook. Try to clear all doubts as soon as possible and aim for a crystal-clear understanding of the concepts rather than mugging up the NCERT text. Refer to Vedantu's Class 11 Physics Chapter 5 Revision Notes for this chapter to understand the chapter well. Practice all the NCERT questions and solve previous year questions from this chapter to perform well in the exam.

6. What are the best Revision Notes for NCERT Class 11 Physics, Chapter 5 - Work, Energy and Power?

The best revision notes for Class 11 Physics , Chapter 5 - “Work, Energy and Power” are Vedantu's Revision Notes. These are the best quality notes for this chapter as they are error-free, credible, and compiled by a team of expert Physics teachers based on the latest syllabus, pattern and marking scheme. These notes are easy to understand and very efficient for revising the maximum syllabus in less time. Revise this chapter from these notes to perform well in the Physics exam. You can access the study material on Vedantu’s App. All the resources are available free of cost.

7. What are the basics of Work, Energy and Power?

Class 11 Physics, Chapter 5 - “Work, Energy and Power” deals with the foundational Physics concepts. The chapter begins with the concept of work in Physics. Then, the chapter discusses energy. Under this, the concepts covered are kinetic energy and potential energy. The law of conservation of energy is discussed next. The other basic concepts discussed in the chapter are power, collision and its types. The application-based numerical problems on the concepts of work, energy and power, conclude the chapter. 

8. What are the real-time applications of Work, Energy and Power?

Work, Energy and Power have several real-time applications. All these three terms are interrelated. We perform a lot of work daily - pushing a car at rest horizontally, driving a truck uphill, a horse pulling the plough across the field etc. Similarly, some real-life instances which require the use of some form of energy are watching television, washing clothes in a washing machine and lighting the home with the help of electricity.

9. What is the law of conservation of energy in reference to Class 11 Chapter 5 ?

In physics, the law of conservation of energy states two things. First, energy is neither created nor destroyed. Second, energy can be converted from one form to another. Thus, the total energy of any object is never lost, and hence, the name of this law is the law of conservation of energy. Therefore, a system has a fixed amount of energy when it is in isolation i.e., no energy is added from an external source of energy.

CBSE Study Materials for Class 11