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Q.
A body of mass $m_{1}$ collides elastically with another body of mass $m_{2}$ at rest. If the velocity of $m_{1}$ after collision becomes $ 2/3 $ times its initial velocity, the ratio of their masses, is
In elastic collision
$v_{1}\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1}+\left(\frac{2 m_{2}}{m_{1}+m_{2}}\right) u_{2}$
If the second ball is at rest, ie, $u_{2}=0$, then
$v_{1}\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1}$
Given $v_{1}=\frac{2}{3} u_{1}$
$\frac{2}{3} u_{1}=\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1}$
$\Rightarrow 2 m_{1}+2 m_{2}=3 m_{1}-3 m_{2}$
$\Rightarrow m_{1}=5 m_{2}$
$\Rightarrow \frac{m_{1}}{m_{2}}=\frac{5}{1}$