A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $${R \over 3}$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

A gramophone record is revolving with an angular velocity $$\omega $$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $$\mu $$. The coin will revolve with the record if

A circular disk of moment of inertia $${I_t}$$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $${\omega _i}$$. Another disk of moment of inertia $${I_b}$$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $$\omega $$. The energy lost by the initially rotating disc to friction is