Question

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

• A. 12 m/s , 6 m/s
• B. 12 m/s , 25 m/s
• C. 6 m/s, 12 m/s
• D. 8 m/s, 20 m/s

Answer 1

Answer: (C)

6 m/s, 12 m/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,

$10\times 10+5\times 4=10v_1+5v_2$

$120=10v_1+5v_2$

$120=10(v_2-6)+5v_2=15v_2-60$

$15v_2=180\Rightarrow v_2=12cm/sec$

$v_1=6cm/sec$