Let a unit vector along the axis of rotation of a purely rotating body and be a unit vector along the velocity of a particle P of the body away from the axis. The value of is

A hollow sphere, a solid sphere, a disc and a ring all having same mass and radius are rolled down on an inclined plane. If no slipping takes place, which one will

take the smallest time to cover a given length?

A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?

A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let be a unit vector along the axis of rotation and be the unit vector along the resultant force on a particle P of the body away from the axis. The value of is

A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin