SYSTEM OF PARTICLES AND ROTATIONAL MOTION
MULTIPLE CHOICE QUESTIONS
1. If a body is rotating about an axis, passing through its centre of mass then its angular momen
tum is directed along its
(a) Radius (b) Tangent
(c) Circumference (d) Axis of rotation Ans: (d)
2. The position of centre of mass of a system of particles does not depend upon the
(a) relative distance between the particles (b) position of the particles
(c) symmetry of the body (d) mass of particles Ans: (a)
3. A man is sitting on a rotating table with his arms stretched outwards.When he suddenly folds
his arms inside, then
(a) his angular velocity will decrease (b) his angular velocity remains constant
(c) his moment of inertia decreases (d) angular momentum increases Ans: (c)
4. The angular momentum of a rigid body is L and its kinetic energy is halved. What happens to
its angular momentum?
(a) L (b) 2L
(c) L/2 (d) L/4 Ans:(d)
5. One circular ring and one circular disc both having same mass and radius. What will be the
ratio of their moment of inertia about the axis passing through their centres and perpendicular
to their planes?
(a) 1 : 1 (b) 2 : 1 (c) 1 : 2 (d ) 1 : 2 Ans:(b)
6. Raw egg and hard boiled eggs are given equal torques,
(a) Raw egg will be rotated faster
(b) Hard boiled egg will be rotated faster.
(c) angular velocity will be same for both.
(d) Can’t say anything. Ans:(b)
7. If an object's angular velocity is increased by 10 per cent, then K.E must be increased by what
percentage?
(a) 40 % (b) 20 % (c) 10 % (d) 21 % Ans:(d)
9. Three point masses m are placed at the vertices of an equilateral triangle of side a. Moment of
inertia of the system about an axis pasing through a mass m at O, and lying in the plane of AOB,
and perpendicular to OA is
2 5 7
(a) 2ma 2 (b) ma 2 (c) ma 2 (d ) ma 2 Ans : (c)
5 4 4
10. A wheel is rotating at the rate of 33 rev min - 1. If it comes to stop in 20 s. Then, the angular
retardation will be
11
(a) rad s -2 (b) 11 rad s -2 (c) rad s - 2 (d) rad s -2 Ans:(d)
200 200
For question numbers 11 to 15, two statements are given-one labelled Assertion and the other la-
belled Reason.Select the correct answer to these questions from the codes (a), (b), (c) and (d) as
given below:
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false and Reason is also false
11. Assertion: Centre of mass of a system does not move under the action of internal forces.
Reason: Internal forces are non-conservative forces. Ans: (c)
12. Assertion: For a system of particles under central force field, the total angular momentum is
conserved.
Reason : The torque acting on such a system is zero. Ans: (a)
13. Assertion: If there is no external torque on a body about its centre of mass, then the velocity of
the centre of mass remains constant.
Reason: Linear momentum of an isolated system remains constant. Ans:(d)
14. Assertion: The angular velocity of a rigid body in motion is defined for the whole body.
Reason: All points on a rigid body performing pure rotational motion are having same angular
velocity. Ans:(b)
15. Assertion (A): Power associated with torque is product of torque and angular speed of the body
about the axis of rotation.
Reason (R): Torque in rotational motion is analogue to force in translatory motion. Ans:(b)
CASE STUDY BASED QUESTIONS
The rotational analogue of force in linear motion is moment of force. It is also referred to as torque
or couple. Force is necessary for a body to do translational motion. Similarly it is the torque which
is required to rotate a body. If net torque applied on the body about the axis of rotation is zero, then
the body doesnot rotate.If a force acts on a single particle at a point, whose position with respect to
the origin is given by the position vector r, the moment of the force acting on the particle with
respect to the origin is defined as the vector product r F .
The magnitude of moment of force is given by r Fsin
(i) Wrench of longer arm is preferred because
(a) It produces maximum force (b) It produces maximum torque.
(c) It is easy to hold (d) Wrench of shorter arm is equally good. Ans:(b)
(ii) The value of M,as shown,for which the rod will be in equilibrium is
(a) 1Kg (b) 2Kg
(c) 3Kg (d) 4Kg
(iii) Let F be the force acting on a particle having position vector r and be the torque of this
force about the origin. Then
(a ) r . F 0 and F. 0 (b) r . 0 and F. 0
(c) r . 0 and F. 0 (d ) r . 0 and F. 0 Ans: (b)
(iv) A body whose moment of inertia is 3 kgm2 ,is at rest. It is rotated for 20 s with a moment of
force 6 Nm.The angular displacement of the body and the work done is
(a) 400 rad and 2400J (b) 200 rad and 2400J
(c) 120 rad and 120J (d) 400 rad 60J Ans: (a)
PRACTICE QUESTIONS
1. A rope of negligible mass is wound around a hollow cylinder of mass 3kg and radius 40cm. What
is the angular acceleration of the cylinder if the rope is pulled with a force of 30N? What is the
linear acceleration of the rope? Consider that no slipping takes place. Ans:(25rads -2 and 10ms-2)
2. Determine which factors affect the moment of inertia of a body.
3. A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and
passing through the centre with a frequency of 10 rotations per second. Calculate the angular
momentum about its axis of rotation. Ans: (2.51 kgm 2/s)
4. From a uniform disc of radius R, a small disc of radius R/2 is cut and removed as shown in the
diagram. Find the center of mass of the remaining portion of the disc.
5. A boat of 90kg is floating in still water. A boy of mass 30 kg walks from the stern to the bow. The
length of the boat is 3 m. Calculate the distance through which the boat will move. (0.75m)
6. A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases from
20 rad s -1 to 40 rad s -1 in 10 seconds. Find the number of rotations in that period. Ans: (150)
7. A metal bar long and in mass supported on two knife-edges placed from
each end. A load is suspended at from one end. Find the reactions at the knife
edges. (Assume the bar to be of uniform cross section and homogeneous). Take
Ans: (54.88N,43.12N)
8.Two solid spheres of the same mass and radius are made of metals of different densities. Which of
them has a larger moment of inertia about a diameter?
9. If earth were to shrink to of its present volume, what would be the new length of the day in
hour? Ans: )
10. Explain if the ice on polar caps of earth melts, how will it affect the duration of the day?
11. Define centre of mass of a system. How does it differ from the centre of gravity?
12. Define angular momentum. Derive the relation between angular momentum and torque.
13.The angular speed of a motor wheel is increased from 1200 rpm to 3210 rpm in 16 seconds. (a)
What is its angular acceleration assuming it to be uniform? (b) How many revolutions does the
engine make during this time?
14. A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53 0 with
it. The other end rests on a rough horizontal floor. Find the normal force,frictional force and
reaction force that the floor exerts on the ladder.
15. Four point masses lie at the corners of a rectangle with sides of length 3 m and 4m. Find the
moment of inertia about each of the diagonals. Take M = 1 kg.
16.The moment of inertia of a uniform circular disc about a tangent of the disc in its own plane is
5
given by MR 2 , where the symbols have their usual meanings.Using this relation, find its M.I.
4
about an axis through its centre and perpendicular to the plane.
17. Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a
square of side b.Find the moment of inertia of the system about an axis about one of the side of
the square.
2
Ans : M 4a 2 5b 2
5
18. The moment of inertia of two rotating bodies A and B are IA and IB. (IA > IB) and their angular
momentum are equal. Which one has greater kinetic enrgy?
19. If the angular momentum of any rotating body increases by 200%, then find the increase in its
kinetic energy.
20. A meter stick is balanced on a knife edge at its Centre. When two coins, each of mass are
put one on top of the other at the mark, the stick is found to be balanced at 45.0cm.
What is the mass of the meter stick? Ans:
21. A child stands at the Centre of a turn table with his arm outstretched. The turn table is set
rotating with an angular speed of 40 rev/min. how much is the angular speed of the child, if he
folds his hand back and thereby reduces his moment of inertia to 2 /5 times the initial value?
Assume that the turntable rotates without friction.
22. A particle performing uniform circular motion has angular momentum .What will be the new
angular momentum, if its angular frequency is doubled and its kinetic energy halved? Ans:
