Question

A ball of mass $10\text{kg}$ is moving with a velocity of $10\text{m/s}$. It strikes another ball of mass $4\text{kg}$, which is moving in the same direction with a velocity of $4\text{m/s}$. If the collision is elastic their velocities after collision will be respectively

• A. $12\text{m/s}$,$10\text{m/s}$
• B. $12\text{m/s}$,$25\text{m/s}$
• C. $6\text{m/s}$,$12\text{m/s}$
• D. $2\text{m/s}$,$20\text{m/s}$

Answer 1

The correct option is C $6\text{m/s}$,$12\text{m/s}$

Let the their velocities after the collision be $v_1$ and $v_2$. As we know for elastic collision.
Relative velocity of approach = relative velocity of speration
$10-4=v_2-v_1\Rightarrow 6=v_2-v_1$
$\Rightarrow v_1=v_2=6$
Applying conservation of momentum,
$10\times 10+5\times 4=10v_1+5v_2$
$120=10v_1+5v_2$
$120=10(v_2-6)+5v_2=15v_2-60$
$15v_2=180\Rightarrow v_2=12\text{cm/sec},$
$v_1=6\text{cm/sec}$