Question

A ball of mass $3\text{kg}$ is moving with velocity $1.5\text{m/s}$ towards a heavy block which is moving towards the ball with velocity $0.5\text{m/s}$ as shown in the figure. Assuming the collision to be elastic, the velocity of the ball immediately after the collision is :

• A. $1.2\text{m/s}$
• B. $2.5\text{m/s}$
• C. $2\text{m/s}$
• D. $3\text{m/s}$

Answer 1

The correct option is B $2.5\text{m/s}$


Now, since the block is given to be heavy,we can assume $m_2>>m_1$
$\Rightarrow m_1+m_2\approx m_2$

So, final velocity of $m_2$ will remain $0.5\text{m/s}$ towards left.
Let velocity of $m_1$ after collision = $v_1$ (towards right)
Now, $e=\frac{v_{separation}}{v_{approach}}=1$ (given)
Taking rightward direction +ve,
$\Rightarrow \frac{v_2-v_1}{u_1-u_2}=1$
$\Rightarrow \frac{-0.5-v_1}{1.5-(-0.5)}=1$
$\Rightarrow v_1=-(2+0.5)=-2.5\text{m/s}$
(-ve sign indicates velocity is towards left)