Question

A ball $A$ of mass $m$ moving along positive $x$ -direction with kinetic energy $K$ and momentum $p$ undergoes elastic head on collision with a stationary ball $B$ of mass $M$ after collision the ball $A$ moves along negative $x$ -direction with kinetic energy $\frac{K}{9}$, final momentum of $B$ is

• A. p
• B. $\frac{p}{3}$
• C. $\frac{4 p}{3}$
• D. 4 p

Answer 1

Answer: (C)

Kinetic energy
$K=\frac{1}{2} m u_{1}^{2}$
$u_{1}=\sqrt{\frac{2 K}{m}} $
$\frac{1}{2} m v_{1}^{2}=\frac{K}{9}$
$v_{1}^{2}=\frac{2 K}{9 \,m} $
Velocity, $ v_{1}=\sqrt{\frac{2 K}{9 \,m}}$ Kinetic energy $K=\frac{p^{2}}{2 m}$
From conservation of the momentum
$m u_{1} =-m v_{1}+p_{B}$
$m\left(u_{1}+v_{1}\right) =p_{B}$
Final momentum of $B$
$p_{B} =m\left[\sqrt{\frac{2 K}{m}}+\sqrt{\frac{2 K}{9 m}}\right] $
$=\sqrt{2 m K}+\sqrt{\frac{2 m K}{3}}=p+\frac{p}{3}=\frac{4 p}{3}$