$A$ ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the track of its centre of mass?

The temperature of a thin uniform circular disc of $1 \ m$ diameter is increased by $10^{\circ} C$. The percentage increase in the moment of inertia of the disc about an axis passing through its centre and perpendicular to the circular face is: (linear coefficient of expansion $\alpha = 11 \times 10^{-6} /{ }^{\circ} C$)

$A$ stick of length $l$ and mass $M$ lies on a frictionless horizontal surface on which it is free to move in any way. $A$ ball of mass $m$ moving with speed $v$ collides elastically with the stick at one of its ends as shown in the figure. If after the collision the ball comes to rest,what should be the mass of the ball?

In the given figure,a ring of mass $m$ is kept on a horizontal surface,and a body of equal mass $m$ is attached through a string wound on the ring. When the system is released,the ring rolls without slipping. Consider the following statements and choose the correct option.
$(i)$ Acceleration of the centre of mass of the ring is $\frac{g}{3}$.
$(ii)$ Acceleration of the hanging particle is $\frac{2g}{3}$.
$(iii)$ Frictional force (on the ring) acts in the forward direction.
$(iv)$ Frictional force (on the ring) acts in the backward direction.

$A$ solid sphere is in purely rotational motion about its diameter. The ratio of its angular momentum $(L)$ and kinetic energy $(K)$ is $\frac{\pi}{22}$. Find the angular velocity $(\omega)$ of the sphere. (Take $\pi = \frac{22}{7}$) (in $rad/s$)

State the equivalent physical quantities in linear motion corresponding to the moment of inertia and torque in rotational motion.