Question

Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially, ball $1$ moves with a speed $u$ towards ball $2$ which is at rest. Immediately after the collision, ball $1$ travels at a speed of $\frac{u}{3}$ in the same direction. What type of collision has occurred?

• A. Inelastic
• B. Elastic
• C. Completely inelastic
• D. cannot be determined from the information

Answer 1

The correct option is B Elastic

Let mass of ball $1=2m$
Mass of ball $2=m$
Velocity of ball 1 before collision $=u$
Velocity of ball 1 after collision $=\frac{u}{3}$
Velocity of ball 2 before collision $=0$
Let final velocity of ball $2=v_2$

As there is no external force on the system, momentum will be conserved.
Applying conservation of linear momentum before and after collision.
$\left(2m\right)u+m\left(0\right)=\left(m\right)v_2+\left(2m\right)\left(\frac{u}{3}\right)$
or $v_2=\frac{4u}{3}$
Now,
$e=\frac{\text{velocity of separation}}{\text{velocity of approach}}$
$e=\frac{v_2-v_1}{u_1-u_2}$
$e=\frac{\frac{4u}{3}-\frac{u}{3}}{u-0}=1$
Hence, collision is elastic.