Question

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

• A. $1:5$
• B. $5:1$
• C. $5:2$
• D. $2:5$

Answer 1

Answer: (B)

$5:1$

Answer 2

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 $v_{1}=\frac{2}{3} u_{1}$ $\frac{2}{3} u_{1}=\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1}$ $\Rightarrow 2 m_{1}+2 m_{2}=3 m_{1}-3 m_{2}$ $\Rightarrow m_{1}=5 m_{2}$ $\Rightarrow \frac{m_{1}}{m_{2}}=\frac{5}{1}$