A ball of mass $10kg$ is moving with a velocity of $10m/s$. It strikes another ball of mass $5kg$, which is moving in the same direction with a velocity of $4m/s$. If the collision is elastic, their respective velocities after the collision will be

The correct option is C $6m/s,12m/s$
Let their velocities after the collision be $v_{1}and{v}_2$. As we know for elastic collision, relative velocity of approach = relative velocity of separation
$10-4=v_2-v_1\Rightarrow 6=v_2-v_1$
$\Rightarrow v_1=v_2-6$
Applying conservation of momentum,
$10\times 10+5\times 4=10v_1+5v_2$
$120=10v_1+5v_2$
$120=10(v_2-6)+5v_2=15v_2-60$
$15v_2=180\Rightarrow v_2=12m/s,$
$v_1=6m/s$
$\Rightarrow v_2=12m/s$