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. $\frac{4p}{3}$
• D. 4 p

Answer 1

Answer: (C)

Kinetic energy
$K=\frac{1}{2}m{u}_1^2$
$u_1=\sqrt{\frac{2K}{m}}$
$\frac{1}{2}m{v}_1^2=\frac{K}{9}$
$v_1^2=\frac{2K}{9m}$
Velocity, $v_1=\sqrt{\frac{2K}{9m}}$ Kinetic energy $K=\frac{p^2}{2m}$
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 $B$
$p_B=m\left[\sqrt{\frac{2K}{m}}+\sqrt{\frac{2K}{9m}}\right]$
$=\sqrt{2mK}+\sqrt{\frac{2mK}{3}}=p+\frac{p}{3}=\frac{4p}{3}$