A ball of mass $m$ moving with speed $v$ collides elastically with an identical stationary ball which is…
A ball of mass $m$ moving with speed $v$ collides elastically with an identical stationary ball which is initially at rest. After collision the first ball moves at an angle $\pi$ to its initial direction and has speed $\left(\frac{v}{3}\right)$. The second ball moves in a straight line after the collision. Then speed of the second ball after collision is
$\frac{2}{\sqrt{3}} v$
$\frac{2 \sqrt{2}}{3} v$
$\frac{4}{3} v$
$\frac{3}{\sqrt{2}} v$
Solution
For elastic collision:
Using energy conservation, $\frac{1}{2} m_1 v_1^2+\frac{1}{2} m_2 v_2^2=\frac{1}{2} m_1 v_1^{\prime 2}+\frac{1}{2} m_2 v_2^{\prime 2}$
Here, $\frac{1}{2} m v^2+0=\frac{1}{2} m(v / 3)^2+\frac{1}{2} m v_2^{\prime 2}$
Or $v_2^{\prime 2}=\frac{8}{9} v^2$
Or $v_2^{\prime}=\frac{2 \sqrt{2}}{3} v$