A constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4\,s$ . The magnitude of this torque is

Two points of a rigid body are moving as shown. The angular velocity of the body is: ?

In the following figure, a body of mass $m$ is tied at one end of a light string and this string and this string is wrapped around the solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$ the system starts moving. If the friction is negligible, angular velocity at time $t$ would be

A mass $‘m’$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

A sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is

When a uniform solid sphere and a disc of the same mass and of the same radius rolls down a rough inclined plane from rest to the same distance, then the ratio of the time taken by them is