Systems of Particles and Rotational Motion Multiple Choice Questions

Q1. For a system to be in equilibrium, the net torques acting on it must balance. This is true only if the torque is taken about 

1. any point on the system
2. The centre of the system.
3. The centre of mass of system.
4. None of these

Answer :- (1)

Q2. Four billiards balls, each of mass 0.5 kg, all are travelling in the same direction on a billiard table, with speeds of 2 m/s, 4 m/s, 8 m/s and 10 m/s.  What is the linear momentum of this system?

1. 10 kg-m/s
2. 2 kg-m/s
3. 5 kg-m/s
4. 12 kg-m/s

Answer :- (4)

Q3. A solid cylinder rolls down an inclined plane of height 6m and reaches the bottom of the plane with angular velocity of 2 rad/s. The radius of the cylinder must be

1. 4 m
2. 4.47 m
3. 5.26 m
4. 5.55 m

Answer :- (2)

Q4. The centre of mass of the Sun, Earth, and Moon system lies

1. between Earth and Moon
2. between Earth and Sun
3. within the Earth
4. within the Sun

Answer :- (4)

Q5. A mass of 10 kg is moving with constant velocity 0.5 m/s parallel to x-axis. The shortest distance of the mass from the origin during its motion is 20-cm. What will be the angular momentum of the mass about the origin in SI unit?

1. zero
2. 0.1
3. 0.5
4. 1

Answer :- (4)

Q6. A torque of 20 Nm is applied to a flywheel of mass 10 kg and radius of gyration 50 cm. The resulting angular acceleration is

1. 8 rads^-2
2. 4 rads^-2
3. 6 rads^-2
4. 10 rads^-2

Answer :- (1)

Q7. Rotational analogue of force of linear motion is

1. Weight
2. Moment of inertia
3. Torque
4. Angular momentum

Answer :- (3)

Q8. A rigid body is rotating about an axis. Different particles are at different distances from the axis. Which of the following is true?

1. Different particles possess the same angular velocity.
2. Different particles possess the same angular acceleration.
3. Different particles possess the same linear velocity.
4. Different particles possess the same linear acceleration.

Answer :- (1)

Q9. kgm²s^-2 is the unit of

1. Torque
2. Force
3. Angular momentum
4. Moment of inertia

Answer :- (1)

Q10. There are two particles of masses m and 2m placed at a distance‘d’ apart  on a smooth horizontal surface. Where will the collision occur (with respect to original positions), if they are allowed to move towards each other because of their mutual attraction?

1. 2d/3
2. 2d
3. d
4. d/2

Answer :- (1)

Q11. A shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in

1. Vertical direction
2. Any direction
3. Horizontal direction
4. Same parabolic path

Answer :- (4)

Q12. The centre of mass of a body is located

1. inside or outside the system
2. inside the system
3. outside the system
4. at the centre of system

Answer :- (1)

Q13. The Earth rotates about an axis passing through its North and South poles with a period of one day. If it is struck by meteorites, then

1. moment of inertia decreases and angular velocity increases
2. moment of inertia increases and angular velocity decreases
3. moment of inertia increases and angular velocity increases
4. moment of inertia decreases and angular velocity decreases

Answer :- (2)

Q14. A small cylinder rolling with a velocity v along a horizontal surface encounters a smooth inclined surface. The height ‘h’ up to which the cylinder will ascend is

1. 3v²/2g
2. 3v²/4g
3. v²/2g
4. v²/4g

Answer :- (3)

Q15.Which of the following is not an example of couple?

1. Compass needle in the earth’s magnetic field
2. Opening the lid of a bottle by turning its finger
3. Balancing a see-saw
4. Increase in the angular velocity of a planet when it comes nearer to the sun.

Answer :- (4)

Q16. Which will roll down a hill faster — a solid cylinder or a solid sphere?

1. Solid cylinder
2. solid sphere
3. Both will reach the ground at the same time
4. Cannot be determined

Answer :- (2)

Q17. A body is moving with a constant velocity parallel to x-axis. Its angular momentum w.r.t origin will

1. remains constant
2. increases
3. decreases
4. become zero

Answer :- (1)

Q18. The angular velocity of the revolution of a planet around the sun increases because

1. Moment of inertia decreases
2. Moment of inertia increases
3. Moment of inertia remains same
4. Moment of inertia has no connection to the angular velocity

Answer :- (1)

Q19. A boy is playing with a tire of radius 0.5m. He accelerates it from 5rpm to 25 rpm in 15 seconds. The linear acceleration of tire is

1. 7 m/s²
2. 10 m/s²
3. 70 m/s²
4. 0.07 m/s²

Answer :- (4)

Q20. Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls, while in air

1. depend on the direction of the motion of the balls.
2. depend on the masses of the two balls.
3. depend on the speeds of the two balls.
4. is equal to g.

Answer :- (4)

Q21. A body is rolling down an inclined plane without slipping. How does the acceleration of the rolling body depend on its radius?

1. It is directly proportional to the radius
2. It is directly proportional to the square root of radius
3. It is inversely proportional to the square root of radius
4. It does not depend upon radius

Answer :- (4)

Q22. A circus acrobat while performing spins brings his limbs closer to the body. Due to this

1. Moment of inertia increases and angular velocity increases
2. Moment of inertia decreases and angular velocity increases
3. Moment of inertia decreases and angular velocity decreases
4. Moment of inertia increases and angular velocity decreases

Answer :- (2)

Q23. A merry- go- round ( diameter 4.0 m ) starts from rest and uniformly accelerates until it rotates at 0.8 rev/min. This occurs in 11s. Once it has reached this rate , it rotates at 0.8 rev/min uniformly . Determine the angular acceleration

1. 0.083 rad/s
2. 0.083 rad/s²
3. 7.55 x 10^-3 rad/s²
4. 6.7 x 10^-3 rad/s²

Answer :- (3)

Q24. Angular momentum is equal to____.(All the symbols used have their usual meanings)

1. L = I²ω
2. L = ma
3. L = I/α
4. L = Iω

Answer :- (4)

Q25. The moment of inertia of a body depends on

1. Shape and Size only
2. Distribution of mass only
3. Position and Orientation of the Axis of rotation only
4. Shape, size, distribution of mass, position and orientation of the axis of rotation.

Answer :- (4)

Q26. In a CO molecule, the distance between carbon and oxygen molecule is 0.12 nm. What is the distance of centre of mass from the carbon atom?

1. 0.02 nm
2. 0.08 nm
3. 0.05 nm
4. 0.07 nm

Answer :- (4)

Q27. If the resultant of all external forces is zero, then velocity of centre of mass will be

1. zero
2. constant
3. maximum
4. minimum

Answer :- (2)

Q28. A ring, a solid cylinder and a solid sphere have been rolled down an inclined plane. Which of them reaches the ground with the least velocity?

1. ring
2. solid cylinder
3. solid sphere
4. all have same velocity

Answer :- (1)

Q29. The moment of momentum is known as

1. torque
2. angular momentum
3. moment of force
4. moment of inertia

Answer :- (2)

Q30. The general motion of a rigid body consists of

1. translational motion only
2. rotational motion only
3. both, translational and rotational motion
4. does not include translational and rotational motions

Answer :- (3)

Q31. The angular momentum of a system of particles is not conserved when

1. net external force acts on the system
2. net external torque acts on the system
3. net external impulse acts on the system
4. none of above

Answer :- (2)

Q32. All the points of a rigid body rotating about the given axis have same :   

1. Linear velocity
2. Angular velocity
3. Linear acceleration
4. Angular momentum

Answer :- (2)

Q33. A sphere cannot roll on

1. a smooth horizontal plane
2. a smooth incline plane
3. a rough horizontal plane
4. a rough incline plane

Answer :- (2)

Q34. Angular velocity is the rate of change of ……………….

1. distance
2. angular distance
3. displacement
4. angular displacement

Answer :- (4)

Q35. The motion of center of mass of a system of two particles is unaffected by their internal forces

1. Irrespective of the actual direction of the internal forces
2. only if they are along the line joining the particles
3. only if they are at right angles to the line joining the particles
4. only if they are obliquely inclined to the line joining the particles

Answer :- (1)

Q36. Two rings have their moment of inertia in the ratio 2:1 and their diameters are in the ratio 2:1. The ratio of their masses will be:

1. 2:1
2. 1:2
3. 1:4
4. 1:1

Answer :- (2)

Q37. The centre of mass is a point

1. which is the origin of reference frame.
2. from which distance of all particles is same.
3. where the whole mass is supposed to be concentrated.
4. which is a geometrical centre of a body.

Answer :- (3)

Q38. There are some passengers inside a stationary railway compartment. The centre of masses of the compartment itself(without the passengers) is C1, while the centre of mass of the compartment plus the passengers’ system is C2. if the passengers move about inside the compartment

1. both C1 and C2 will move with respect to the ground
2. neither C1 nor C2 will move with respect to the ground
3. C1 will move but C2 will be stationary with respect to the ground.
4. C2 will move but C1 will be stationary with respect to the ground.

Answer :- (3)

Q39. A rigid body is said to be in mechanical equilibrium if

1. net force on the rigid body is zero
2. net torque on the rigid body is zero
3. either net force or net torque on the rigid body is zero
4. both net force and net torque on the rigid body is zero

Answer :- (4)

Q40. Every point in a rotating rigid body has the same __________at any instant of time.

1. linear velocity
2. angular velocity
3. linear momentum
4. displacement

Answer :- (2)