Question

A small ball of mass $10\text{kg}$ moving with initial velocity of $4\text{m/s}$ collides head on with a heavy iron ball initially moving with velocity $0.2\text{m/s}$ as shown in the figure below. The velocity of $10\text{kg}$ mass after collision will be approximately (Assume collision to be perfectly elastic)

• A. $4.4\text{m/s}$
• B. $3.6\text{m/s}$
• C. $3\text{m/s}$
• D. $2.8\text{m/s}$

Answer 1

The correct option is B $3.6\text{m/s}$

Given $u_1=4\text{m/s},u_2=0.2\text{m/s}$
The small ball has very less mass compared to the iron ball. Also, collision is perfectly elastic (given).

Therefore, iron ball will continue to move at $0.2\text{m/s}$ even after head on collision with $10\text{kg}$ ball.

So, $v_2=0.2\text{m/s}$ (towards right)

Let velocity of the small ball be $v_1$ (towards left) after collision.

Now, $e=1=\frac{v_{separation}}{v_{approach}}$
$\Rightarrow \frac{-v_1-0.2}{0.2-4}=1$
$\Rightarrow v_1=3.8-0.2=3.6\text{m/s}$ (towards left)