Question

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

• A. $\frac{2v}{3}$
• B. $\frac{v}{2}$
• C. $\frac{\sqrt{3}v}{2}$
• D. $v$

Answer 1

The correct option is C $\frac{\sqrt{3}v}{2}$

Collision is elastic.

Hence velocities along the line of impact will be exchanged.

Velocity of particle along line of impact $=Vcos\theta$

$⟹\frac{v\sqrt{R^2-\left(\frac{R}{2}\right)}}{R}$

$⟹\frac{v\sqrt{3}}{2}$

Velocity of particle perpendicular to the line of impact:

$⟹Vsin\theta =\frac{v}{2}$

Velocity of the disc $=\frac{v\sqrt{3}}{2}$