A sphere of mass m falls on a smooth hemisphere of mass M resting with its plane face on smooth horizontal table, so that at the moment of impact, line joining the centres makes an angle with the vertical. The velocity of sphere just before impact is u and e is the coefficient of restitution.

A smooth wedge of mass M is kept at rest on a smooth horizontal surface . Inclined face of the wedge make an angle theta with the horizontal . A particle of mass m collides normal to inclined face of wedge . If speed of the particle just before collision is u and coefficient of restitution is e then find velocity of wedge after collision .

Two equal spheres of mass m are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and reduces to rest. Then:

A sphere of mass 'm' moving with velocity 'v' collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)

A sphere of mass 'm' moving with velocity 'v' collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)

A smooth hemisphere of mass m and radius R is at rest. A smooth solid sphere of mass 2m and radius R moving with velocity V_(0) between two horizontal smooth surfaces separated by a distance slightly greater than 2R as shown in figure. Solid sphere collides with the hemisphere. if coefficient of restitution is (1)/(2) , then

A smooth hemisphere of mass m and radius R is at rest. A smooth solid sphere of mass 2m and radius R moving with velocity V_(0) between two horizontal smooth surfaces separated by a distance slightly greater than 2R as shown in figure. Solid sphere collides with the hemisphere. if coefficient of restitution is (1)/(2) , then

A sphere of mass m , impinges obliquely on a sphere, of mass M, which is at rest. Show that, if m=eM , the directions of motion of the sphere after impact are at right angles.

A sphere of mass m , impinges obliquely on a sphere, of mass M, which is at rest. Show that, if m=eM , the directions of motion of the sphere after impact are at right angles.