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

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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.

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