Question

A heavy ring of mass m is clamped on the periphery of al light circular disc. A small particle having equal mass is clamped at the centre of the disc. The system is rotated in such a way that the centre moves in a circle of radius r with a uniform speed v. We conclude that an external force
(a) $\frac{m{v}^2}{r}$ must be acting on the central particle
(b) $\frac{2m{v}^2}{r}$ must be acting on the central particle
(c) $\frac{2m{v}^2}{r}$ must be acting on the system
(d) $\frac{2m{v}^2}{r}$ must be acting on the ring.

Answer 1

(c) $\frac{2m{v}^2}{r}$ must be acting on the system

Total mass of the system = 2m
To move the centre of the system in a circle of radius r with a uniform speed v, the external force required is $\frac{2m{v}^2}{R}$.