KENDRITYA VIDYALAYA

SANGATHAN
KVS RO KOLKATA
SESSION 2023-24
STUDY MATERIAL FOR SLOW
ACHIEVERS
CLASS-XI PHYSICS
CHAPTER:7 MOTION OF SYSTEM
OF PARTICLES AND RIGID BODY

Q CORE QUESTION MARK

NO. CONCEPT
/
FOCUSED-
FORMUL
A/
TARGATE
D
THEORE
M
SECTION -A: MCQ (QN NO 1-15)
1 Torque and When a torque acting on a system is zero, then which of the following 1
angular should not change?
momentum (a) Linear velocity
(b) Angular momentum
(c) Angular displacement
(d) Force acting on the body
2 𝜏⃗ = 𝑟⃗⃗⃗ x 𝐹⃗ The torque of a force 𝐹⃗ = 3𝑖̂ + 𝑗̂ + 5 𝑘̂ acting at the point 𝑟⃗⃗⃗ = 7𝑖̂ + 3 𝑗̂ + 1
𝑘̂ is
(a) 14𝑖̂ - 38 𝑗̂ + 16 𝑘̂
(b) 4𝑖̂ - 38 𝑗̂ + 6 𝑘̂
(c) 21𝑖̂ + 4 𝑗̂ + 4 𝑘̂
(d) −14𝑖̂ + 38 𝑗̂ - 16 𝑘̂
3 Moment of Two rings have their moments of inertia in the ratio 2 : 1 and their 1
inertia of diameters are in the ratio 2 : 1. The ratio of their masses will be
ring = MR2 (a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 1 : 1
4 Velocity of Two identical particles moves towards each other with velocities 2V and 1
centre of V respectively. The velocity of centre of mass is
mass (a) V
(b) V/3
(c) V/2
(d) Zero
5 Center of The X and Y coordinates of the three particles of masses m, 2m and 3m 1
Mass are respectively (0,0) (1,0) and (–2,0). The X-coordinate of the centre of
mass of the system is
(a) 1 /3
(b) 2/ 3
(c) -1 /3
(d) -2/ 3
6 Moment of Moment of inertia depends on 1
inertia (a) Distribution of particles
(b) Mass
(c) Position of axis of rotation
(d) All of these
7 Conservatio If a gymnast, sitting on a rotating stool, with his arms outstretched, 1
n of angular suddenly lowers his hands
momentum (a) the angular velocity increases
(b) his moment of inertia increases
(c) the angular velocity stays constant
(d) the angular momentum increases
8 Rotational A 40kg flywheel in the form of a uniform circular disc of diameter 1m is 1
kinetic making 120 rpm . The Kinetic energy of rotation of flywheel is (Take 𝜋 2
energy = 10)
(a) 20 J
(b) 200 J
(c) 400 J
(d) 800 J
9 Motion of A cracker travelling in parabolic path under the effect of gravity explodes 1
centre of in mid air. The centre of mass of the fragments will
mass (a) move in straight path
(b) move vertically downward
(c) move in parabolic path, the unexploded cracker will have travelled
(d) move in vertically upward and then vertically downward.
10 An automobile engine develops 100 kW when rotating at a angular speed 1
Power in of 250 rad /s. What torque does it deliver
rotational (a) 350 N-m
motion (b) 400 N-m
(c) 450 N-m
(d) 628 N-m
11 Position of The centre of mass of a body: 1
centre of (a) Lies always at the geometrical centre
mass (b) Lies always inside the body
(c) Lies always outside the body
(d) May lie within or outside the body
12 Relation Two bodies have their moment of inertia I and 2I respectively about their 1
between axis of rotation. If their kinetic energies of rotation are equal, their angular
moment of momentum will be in the ratio
inertia and (a) 1 : 2
kinetic (b) √2 : 1
energy (c) 2 : 1
(d) 1 : √2
13 Angular The angular momentum of a particle describing uniform circular motion is 1
momentum L. If its kinetic energy is halved and angular velocity doubled, its new
and kinetic angular momentum is
energy (a) 4 L
(b) L / 4
(c) L /2
(d) 2L

14 Example of Planetary motion in the solar system describes 1

conservation (a) Conservation of kinetic energy
of angular (b) Conservation of linear momentum
momentum (c) Conservation of angular momentum
(d) All of the above
15 Direction of When a mass is rotating in a plane about a fixed circular path its angular
angular momentum is directed along
momentum (a) a line perpendicular to the plane of rotation
(b) the radius of the circle
(c) the tangent to the circle
(d) a line makimg an angle 450 to the plane of rotation.
SECTION -B: ASSERTION REASONING QUESTIONS: (QN NO 1
16-20)
Assertion: (A). 1
Reason: (R)
CHOOSE THE CORRECT OPTION AS PER THE STATEMENTS
GIVEN IN ASSERTION AND REASON:
a) Assertion and Reason both are correct and R is the correct explanation
of A.
b) Assertion and Reason both are correct but R is not the correct
explanation of A.
c) Assertion is true but Reason is false.
d) Assertion is wrong statement but reason is correct statement.
16 Appllication Assertion (A) : If polar ice melts, days will be longer. 1
of Reason (R) : Moment of inertia decreases and these angular velocity
conservation increases
of angular
momentum
17 Mass and Assertion (A) : The centre of mass of a body may lie where there is no 1
centre of mass. Reason (R) : The centre of mass has nothing to do with the mass of
mass the body.
18 Direction of Assertion (A) : Torque is a vector whose direction is along the applied 1
torque force. Reason (R) : 𝜏⃗=𝑟⃗ x 𝐹⃗
19 Angular Assertion (A) : The angular velocity of earth around the sun increase 1
velocity and when it comes closer to the sun.
moment of Reason (R) : Angular velocity is directly proportional to the moment of
inertia inertia when the angular momentum is constant.
20 Appllication Assertion (A) : The speed of a whirl wind in tornado is alarmingly high. 1
of Reason (R) : If no external torque acts on a body, its angular velocity
conservation remains constant
of angular
momentum
SECTION -C: CREATIVE AND CRITICAL THINKING
QUESTIONS: (QN NO 21-22)
21 Location of From a uniform disk of radius R, a circular hole of radius R/2 is cut out. 1
centre of The centre of the hole is at R/2 from the centre of the original disc. Locate
mass the centre of mass of the resulting flat body.

22 Kinetic A particle performs uniform circular motion with an angular momentum 1

energy and L. If the frequency of particle’s motion is doubled and its K.E is halved,
frequency what happens to the angular momentum?
SECTION -D: VERY SHORT ANSWER QUESTIONS: (QN NO 23-
29)
 FREQUENTLY ASKED QUESTIONS: [Qn 23-26]
23 Theorem of State the theorem of parallel and theorem of perpendicular axes of 2
moment of moment of inertia.
inertia
24 Application How will you distinguish between a hard boiled egg and a raw egg by 2
of moment spinning each on a table top?
of inertia
25 Conservatio A block hangs from a string wrapped on a disc of radius 20 cm free to 2
n of energy rotate about its axis which is fixed in a horizontal position. If the angular
speed of the disc is 10 rad/s at some instant, with what speed is the block
going down at the instant?
26 Moment of Two solid spheres of the same mass are made of metals of different 2
inertial and densities. Which of them has a large moment of inertia about the diameter
density of ?
material
MOST IMPORTANT QUESTIONS (AS PER CONCEPT/ LEARNING
OUTCOME OF THE CHAPTER) [Qn 27-29]
27 Definition Define moment of inertia. Give its unit. State two factors on which the 2
of moment moment of inertia depends.
of inertia
28 Equilibrium When does a rigid body said to be in equilibrium ? State the necessary 2
of rigid condition for a body to be in equilibrium.
body
29 Radius of Calculate radius of gyration of a cylindrical rod of mass m and length L 2
gyration and about an axis of rotation perpendicular to its length and passing through
moment of the centre.
inertia.
SECTION -E: SHORT ANSWER QUESTIONS: (QN NO 30-36)
FREQUENTLY ASKED QUESTIONS: (Qn 30-33) 3
30 Work done Obtain an expression for the work done by a torque. Hence write the
in rotational expression for power.
motion.
31 Conservatio If the radius of the earth contracts to half of its present day value without 3
n of angular change in mass, Find the length of the day?
momentum
32 Equation of The angular speed of a motor wheel is increased from 1200 rpm to 3120 3
rotational rpm in 16 seconds, (i) What is its angular acceleration (assume the
motion acceleration to be uniform) (ii) How many revolutions does the wheel
make during this time ?
33 L = Iω Name the physical quantity is conserved when a planet revolves around 3
the sun ? Obtain the relation of the physical quantity with the moment of
inertia.
MOST IMPORTANT QUESTIONS (AS PER CONCEPT/ LEARNING
OUTCOME OF THE CHAPTER) (Qn 34-36)
34 Appliation The moment of inertia of a disc of mass M and radius R about an axis 3
of Theorem 1
through the centre and perpendicular to its plane is 2 𝑀𝑅 2 . Obtain the
of moment
expression for the moment of inertia of the disc about (a) its diameter (b)
of inertia
a tangent in its plane.
35 Proof of Derive the three equation of rotational motion 3
equation of (i) ω = ω0 + αt (ii) 𝜃 = 𝜔0 𝑡 + 1⁄2 𝛼𝑡 2
rotational (iii) ω2 = 𝜔0 2 +2 𝛼 𝜃
motion
36 Angular Define Angular momentum. Prove that the rate of change of angular 3
momentum momentum of a system of particles about a reference point is equal to the
and torque net torque acting on the system.
 SECTION -F: CASE STUDY BASED QUESTIONS: (QN NO 37-38)
37 Couple 4

A magnetic needle is used to show the show geographic North-South

direction.
The earth’s magnetic field exerts equal forces on the north and south
poles. The force on the North Pole is towards the north, and the force on
the South Pole is toward the south. the two forces do not have the same
line of action. Thus there is a couple acting on the needle due to the
earth’s magnetic field.

(a) What is the net force acting on the magnetic dipole.

(b) What is couple ? What is the effect of couple on a body.
(c) Show that the moment of couple is same irrespective of the point of
rotation of a body.

38 Conservatio Read the following passage and choose appropriate answers of questions 4
n of angular 1 to 4.
momentum The time rate of the total angular momentum of a system of particles
about a point (taken as the origin of our frame of reference) is equal to the
sum of the external torques (i.e. the torques due to external forces) acting
on the system taken about the same point.
𝜏𝑒𝑥𝑡 = 𝑑𝐿/ 𝑑𝑡
If 𝜏𝑒𝑥𝑡 =0
𝑑𝐿/𝑑𝑡 =0 or L = constant.
Or 𝐼𝜔 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛t
Thus, if the total external torque on a systemof particles is zero, then the
total angularmomentum of the system is conserved, i.e.remains constant.
With the help of above comprehension, choose the most appropriate
alternative for each of the following questions:
1. Which of the following can be explained with the help of conservation
of angular momentum?
a. Driving
b. Ice- skating
c. Diving
d. running
2. For angular momentum to be conserved what must be true about the
net torque of the system?
a. Net torque is constant.
b. Net torque increases.
c. Net torque decreases.
d. Net torque is zero.
3. A person sits on a freely spinning lab stool that has no friction in its
axle. When this person extends her arms:
a. her moment of inertia increases and her angular speed decreases
b. her moment of inertia decreases and her angular speed increases.
c. her moment of inertia increases and her angular speed increases.
d. her moment of inertia increases and her angular speed remains the
same.
 4. Two children, Ahmed and Saleh, ride on a merry-go-round. Ahmed is
at a greater distance from the axis of rotation than Saleh. Which of the
following are true statements?
a. Saleh and Ahmed have the same tangential speed.
b. Ahmed has a greater tangential speed than Saleh.
c. Saleh has a greater angular speed than Ahmed.
d. Saleh has a smaller angular speed than Ahmed
SECTION -G: LONG ANSWER QUESTIONS: (QN NO 39-40)
39 Torque and (i) Establish the relation between torque and angular acceleration. Hence
angular define moment of inertia. 5
acceleration (ii) Show that the angular momentum about any point of a single particle
moving with constant velocity remains constant throughout the motion.
(i) Why is it more difficult to revolve a stone by tying it to a longer
string than by tying it to a shorter string ?
(ii) A cat is able to land on its feet after a fall. Why ?
40 Relation of (i) With the help of diagram show that torque is equal to the product of 5
torque and force and the perpendicular distance of its line of action form the axis of
its rotation.
application Also explain that radial component of force has nothing to do with the
torque.
(ii) Why is it more difficult to revolve a stone by tying it to a longer
string than by tying it to a shorter string?

ANSWER KEY:
Q.NO. Answer MARK
SECTION -A: MCQ (QN NO 1-15) [Answer explanation]
1 (b) Angular momentum 1
2 (a) 14𝑖̂ - 38 𝑗̂ + 16 𝑘̂ 1
3 (b) 1 : 2 1
4 (c) V/2 1
5 (d) -2/ 3 1
6 (d) All of these 1
7 (a) the angular velocity increases 1
8 (c) 400 J 1

9 (c) Angular momentum 1

10 b) 400 Nm 1
11 (d) 1
12 (d) 1 : √2 1
13 (b) L/4 1
14 (c) Conservation of angular momentum 1
15 (a) 1
SECTION -B: ASSERTION REASONING QUESTIONS: (QN NO 16-20)
16 (c) A is true but R is false. When ice melts, MI increases and hence angular velocity 1
decreases. L = Iw = constant
17 (c) A is true but R is false. CM depends upon the distribution of mass 1
18 d) Assertion is wrong statement but reason is correct statement 1
19 (c) A is true but R is false. 1
20 angular momentum becomes one fourth. (c) here assertion is true but reason is false. 1
Assertion is true as per conservation of angular momentum but when no external torque
acts on the body, they its angular momentum is constant not angular velocity
SECTION -C: CREATIVE AND CRITICAL THINKING QUESTIONS: (QN NO
21-22)