A small body of mass 'm' is placed at the top of a smooth sphere of radius 'R' placed on a horizontal surface as shown, Now the sphere is given a constant horizontal acceleration `a_(0) = g`. The velocity of the body relative to the sphere at the moment when it loses contact with the sphere is

A small body is placed on the top of a smooth sphere of radius R. Then the sphere is imparted a constant acceleration w_0 in the horizontal direction and the body begins sliding down. Find: (a) the velocity of the body relative to the sphere at the moment of break-off, (b) the angle theta_0 between the vertical and the radius vector drawn from the centre of the sphere to the break-off point, calculate theta_0 for w_0=g .

A unofrom rope of mass m is placeced on a smooth fixed sphere of radius R as shown in the figure .Find the tension T in the rope when it is in a horizontal plane at a vertical distance h=R/2 below the top of the sphere .

Three identical spheres each of radius 'R' are placed on a horizontal surface touching one another. If one of the spheres is removed, the shift in the centre of mass of the system is.