A particle of mass m strikes elastically with a disc of radius R, with a velocity $\overrightarrow {v}$ as shown. If the mass of the disc is equal to that of the particle and the surface of contact is smooth, then the velocity of disc just after the collision is

Question

$$\begin {array} {1 1} (a)\;\frac{2v}{3} & \quad (b)\;\frac{v}{2} \\ (c)\;\frac{\sqrt {3} v}{2} & \quad  (d)\;v \end {array}$$