Question

A stone of mass $m$ is thrown with a velocity $u$ at a block of mass $M$ which is initially at rest. The collision between the bodies is elastic. If the final velocities of the stone and the block are in the ratio $-4:1$, then what is the ratio of the mass of the stone to the mass of the block?

• A. $3:2$
• B. $2:3$
• C. $1:1$
• D. $1:9$

Answer 1

The correct option is D $1:9$

Given,

$u_1=u,u_2=0$
$\frac{v_1}{v_2}=\frac{-4}{1}$
$\begin{array}{}{v}_1=-4v_2& \text{(1)}\end{array}$
As we know, the relative speed of approach is the same as the relative speed of separation in elastic collision
$u_1-u_2=v_2-v_1$
$u=v_2+4v_2$
$\begin{array}{}u=5v_2& \text{(2)}\end{array}$
By using conservation of energy
$\begin{array}{}mu+M{u}_2=m{v}_1+M{v}_2& \text{(3)}\end{array}$
From equation 1 and 2 in equation 3 we get,
$m\left(5v_2\right)=m(-4v_2)+M{v}_2$
Dividing above equation by $M{v}_2$
$\frac{m}{M}5=-\frac{m}{M}4+1$
$\frac{m}{M}(5+4)=1$
$\frac{m}{M}=\frac{1}{9}$