A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram.

The angular velocity '$$\omega$$' of the ball will be [ $$\mathrm{T}=$$ Tension in the string.]

A particle performing uniform circular motion of radius $$\frac{\pi}{2} \mathrm{~m}$$ makes '$$\mathrm{x}$$' revolutions in time '$$t$$'. Its tangential velocity is

A body of mass 200 gram is tied to a spring of spring constant $$12.5 \mathrm{~N} / \mathrm{m}$$, while other end of spring is fixed at point '$$O$$'. If the body moves about '$$O$$' in a circular path on a smooth horizontal surface with constant angular speed $$5 \mathrm{~rad} / \mathrm{s}$$ then the ratio of extension in the spring to its natural length will be

A particle of mass '$$\mathrm{m}$$' moves along a circle of radius '$$r$$' with constant tangential acceleration. If K.E. of the particle is '$$E$$' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is