Unit – 5 : Motion of System of Particles and Rigid Bodies

1. The centre of mass of a system of particles does not depend upon

a) position of particles
b) relative distance between particles
c) masses of particles
d) force acting on particle
Answer: d)

2. A couple produces

a) pure rotation
b) pure translation
c) rotation and translation
d) no motion
Answer: a)

3. A particle is moving with constant velocity along a line parallel to the positive X-axis. The magnitude of its angular momentum about the origin is

a) zero
b) increasing with $x$
c) decreasing with $x$
d) remaining constant
Answer: d)

4. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. If the rope is pulled with a force of 30 N, the angular acceleration of the cylinder is

a) 0.25 rad s$^{-2}$
b) 25 rad s$^{-2}$
c) 5 m s$^{-2}$
d) 25 m s$^{-2}$
Answer: b)

5. A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

a) increases
b) decreases
c) remains constant
d) depends on direction of rotation
Answer: a)

6. A rigid body rotates with angular momentum $L$. If its kinetic energy is halved, the angular momentum becomes

a) $L$
b) $L/2$
c) $2L$
d) $L/\sqrt{2}$
Answer: d)

7. A particle undergoes uniform circular motion. The angular momentum of the particle remains conserved about

a) centre of the circle
b) a point on the circumference
c) any point inside the circle
d) any point outside the circle
Answer: a)

8. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

a) line perpendicular to the plane of rotation
b) line making $45^\circ$ with plane
c) radius
d) tangent to the path
Answer: a)

9. Two discs of same moment of inertia rotating with angular velocities $\omega_1$ and $\omega_2$ are brought into contact. The loss of energy is

a) $\frac14 I(\omega_1-\omega_2)^2$
b) $I(\omega_1-\omega_2)^2$
c) $\frac18 I(\omega_1-\omega_2)^2$
d) $\frac12 I(\omega_1-\omega_2)^2$
Answer: a)

10. A disc of moment of inertia $I_a$ rotating with angular speed $\omega$ is dropped coaxially on another disc of moment of inertia $I_b$. The loss of kinetic energy is

a) $\frac12\frac{I_b^2}{I_a+I_b}\omega^2$
b) $\frac{I_b^2}{I_a+I_b}\omega^2$
c) $\frac{(I_b-I_a)^2}{I_a+I_b}\omega^2$
d) $\frac12\frac{I_b I_a}{I_a+I_b}\omega^2$
Answer: d)

11. The ratio of acceleration for a solid sphere rolling without slipping and slipping without rolling down an incline is

a) 5:7
b) 2:3
c) 2:5
d) 7:5
Answer: a)

12. From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$ is cut. The moment of inertia of the remaining part is

a) $\frac{15MR^2}{32}$
b) $\frac{13MR^2}{32}$
c) $\frac{11MR^2}{32}$
d) $\frac{9MR^2}{32}$
Answer: b)

13. The speed of a solid sphere rolling without slipping down an incline of vertical height $h$ is

a) $\sqrt{\frac43 gh}$
b) $\sqrt{\frac{10}{7}gh}$
c) $\sqrt{2gh}$
d) $\sqrt{\frac12 gh}$
Answer: b)

14. The speed of the centre of a rolling wheel is $v_0$. The speed of a point on the rim at the top is

a) zero
b) $v_0$
c) $\sqrt2 v_0$
d) $2v_0$
Answer: c)

15. A round object rolls down an inclined plane without slipping. The frictional force

a) dissipates energy as heat
b) decreases rotational motion
c) decreases translational and rotational motion
d) converts translational energy into rotational energy
Answer: d)