Question

Particle $A$ makes a perfectly elastic collision with another stationary particle $B$ . They fly apart in opposite directions with equal velocities. The mass ratio will be

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (A)

Let $m_{1}$ and $m_{2}$ be the masses of the particles.
By the principle of conservation of momentum,
$m_{1}u_{1}+0=m_{2}v-m_{1}v$ ..... (i)
$\because e=1$
$2v=u_{1}$
Substituting this in (i)
$2m_{1}v=m_{2}v-m_{1}v$
$2m_{1}=m_{2}-m_{1}$
$3m_{1}=m_{2}$
$\frac{m_{1}}{m_{2}}=\frac{1}{3}$