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 $v$ towards ball $2$ which is at rest. Immediately after the collision, ball $1$ travels at a speed of $\frac{v}{3}$ in the same direction. What type of collision has occured ?

• A. Inelastic
• B. Elastic
• C. Completely Inelastic
• D. Cannot be determined from the information given

Answer 1

The correct option is B Elastic


Let mass of ball $2$ is $m$ and mass of ball $1$ is $2m$.
final velocity of ball $\left(1\right)$ after collision
$v_1=\frac{(m_1-e{m}_2)u_1+m_2(1+e)u_2}{m_1+m_2}$
Given $u_1=v,u_2=0$
$v_1=\frac{(m_1-e{m}_2)v}{m_1+m_2}$

Substituting masses
$v_1=\frac{(2m-me)v}{2m+m}$
$\frac{v}{3}=\frac{(2-e)v}{3}$
$1=2-e$
$\Rightarrow e=1$
So collision is elastic in nature.