Question

A sphere of mass $m_1=2kg$ collides with a sphere of mass $m_2=3kg$ which is at rest. Mass $m_1$ will move at right angle to the line joining centres at the time of collision, if the coefficient of restitution is

• A. $\frac{4}{9}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $\sqrt{\frac{2}{3}}$

Answer 1

Answer: (C)

$\frac{2}{3}$

Let the velocity of $m_{1}be{v}_1$ and and final velocity $m_{2}be{v}_2$

Conserving momentum in horizontal direction, we get

$m_1{v}_1=m_2{v}_2\Rightarrow 2\times v_1=3\times v_2$

Coefficient of restitution $e=\frac{velocityofseparation}{velocityofapproach}=\frac{v_2}{v_1}$

So $e=\frac{2}{3}$