A hemisphere of radius R and mass 4 m is free to slide with its base on a smooth horizontal table . A particle of mass m is placed on the top of the hemisphere . The angular velocity of the particle relative to centre of hemisphere at an angular displacement `theta` when velocity of hemisphere has become v is

A particle is released from the top of the smooth hemisphere R as shown. the normal contact between the particle and the hemisphere in position theta is

A particle of mass m is released from the top of a smooth hemisphere of radius R with the horizontal speed mu . Calculate the angle with verticle where it loses contact with the hemisphere.

A particle of mass m slides down from the vertex of semi- hemisphere, without any initial velocity. At what height from horizontal will the particle leave the sphere-

A partcle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down :

A partcle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down :

A small particle rests on the top of a hemisphere of radius 20 cm. The smallest horizontal velocity given to it, if it is to leave the hemisphere without sliding down along its surface, is

A disc of mass m and radius R lies flat on a smooth horizontal table. A particle of mass m, moving horizontally along the table, strikes the disc with velocity V while moving along a line at a distance (R)/(2) from the centre. Find the angular velocity acquired by the disc if the particle comes to rest after the impact.