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

$\begin {array} {1 1} (a)\;\frac{4}{9} & \quad (b)\;\frac{1}{2} \\ (c)\;\frac{2}{3} & \quad (d)\;\sqrt {\frac{2}{3}} \end {array}$

By momentum conservation along the line of impact.
$m_1u_1 \cos \theta=m_2 v_2$
By Newton's law of restitution
$\large\frac{V_2}{u_1 \cos \theta}$$=e$
$\large\frac{V_2}{u_1 \cos \theta}=\frac{m_1}{m_2}$
$\qquad= \large\frac{2}{3}$