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# 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

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

Collision is elastic.
Hence velocities along the line of impact will be exchanged.
Velocity of particle along line of impact $=V \cos \theta$
$\qquad= \large\frac{V \sqrt {R^2-\bigg(R/2 \bigg)}}{R}$
$\qquad= \large\frac{V \sqrt 3}{2}$
Velocity of particle perpendicular to line of impact
$V \sin \theta= v \times \large\frac{1}{2}$
Velocity of disc $=\large\frac{ v \sqrt 3}{3}$
Particles will move perpendicular to disc.