We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by

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

In the figure shown a ring $A$ is initially rolling without sliding with a velocity $v$ on the horizontal surface of the body $B$ (of same mass as $A$). All surfaces are smooth. $B$ has no initial velocity. What will be the maximum height reached by $A$ on $B$.

A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of free end of the stick if the string is cut? (in $rad/sec^2$ )

Four masses are fixed on a massless rod as shown in Fig. The moment of inertia about the axis $P$ is about ....... $kg-m^2$

Three thin metal rods, each of mass $M$ and length $L$ are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is