$A$ body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the top point of the body. If the body rolls purely on the surface,its shape can be:

If the earth suddenly contracts to $(1/3)^{rd}$ of its present size without any change in its mass, the ratio of the kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself).

$A$ thin ring of mass $2 \ kg$ and radius $1 \ m$ is rolling without slipping on a horizontal plane with velocity $1 \ m/s$. $A$ small ball of mass $1 \ kg$,moving with velocity $2 \ m/s$ in the opposite direction,hits the ring at a height of $1.8 \ m$ and goes vertically up with velocity $1 \ m/s$. Immediately after the collision:
$(A)$ the ring has pure rotation about its stationary $CM$.
$(B)$ the ring comes to a complete stop.
$(C)$ friction between the ring and the ground is to the left.
$(D)$ there is no friction between the ring and the ground.

$A$ thin string is wrapped around the circumference of a wheel of radius $r$. The wheel has a horizontal axle and a moment of inertia $I$ about it. $A$ weight $mg$ is attached to the end of the string,which falls from rest. After falling through a distance $h$,the angular velocity of the wheel will be:

Choose the correct statement.

Four point masses are fastened to the corners of a frame of negligible mass lying in the $xy$ plane as shown in the figure. Let $\omega$ be the angular speed of rotation. Then: