Question

A moving body with a mass $m_1$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ should be in the ratio so as to decrease the velocity of the first body 1.5 times, assuming a perfectly elastic impact. Then, the ratio $m_1:m_2$ is :

• A. $\frac{1}{25}$
• B. $\frac{1}{5}$
• C. $5$
• D. $25$

Answer 1

The correct option is C $5$

Let masses be $m,km$
Let initial velocity be $v.$ vel of $m$ after collision be $\frac{v}{1.5}=\frac{2v}{3}$
conservation of momentum $mv=\frac{2mv}{3}+km{v}_1$
$v_1=\frac{v}{3k}$
For elastic collision$,e=1$
$v=\frac{v}{3k}-\frac{2v}{3}$
$k=\frac{1}{5}$
Ratio is $1:1/5$ i.e.$,5:1$