$A$ same torque is applied to a disc and a ring of equal mass and radii. Then:

$A$ wheel is rotating at $600$ rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in rad/s$^2$ is (retardation is uniform).

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

$A$ body rotating at $20 \ rad/s$ is acted upon by a constant torque providing it a deceleration of $2 \ rad/s^2$. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

$A$ wheel has a moment of inertia $5 \times 10^{-3} \, kg \, m^2$ and is making $20 \, rev/sec$. The torque needed to stop it in $10 \, sec$ is $............. \times 10^{-2} \, N-m$. (in $\pi$)

An automobile moves on a road with a speed of $54 \,km h^{-1}.$ The radius of its wheels is $0.45\, m$ and the moment of inertia of the wheel about its axis of rotation is $3\, kg m^2$. If the vehicle is brought to rest in $15\, s,$ the magnitude of average torque transmitted by its brakes to the wheel is .......... $kg \,m^2\, s^{-2}$.