Two bodies of masses '$$\mathrm{m}$$' and '$$3 \mathrm{~m}$$' are rotating in horizontal speed of the body of mass '$$m$$' is $$n$$ times that of the value of heavier body; while the centripetal force is same for both. The value of $$n$$ is

A particle is moving along the circular path with constant speed and centripetal acceleration 'a'. If the speed is doubled, the ratio of its acceleration after and before the change is

A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $$\frac{V}{2}$$ and radius is increased to '3r'. For this change, initial centripetal force needs to be

A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [$$\mathrm{g}=$$ acceleration due to gravity]