Question

A ball 'A' of mass ${}^{\prime }{m}^{\prime }$ moving along positive x-direction with kinetic energy ${}^{\prime }{K}^{\prime }$ and momentum $P$ undergoes elastic head on collision with a stationary ball B of mass ${}^{\prime }{M}^{\prime }$. 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. $4P$

Answer 1

The correct option is C $\frac{4P}{3}$

Let the magnitudes of final momenta of $A$ and $B$ be $P_1,P_2$.

$K=\frac{P^2}{2m}$

Thus $P=P_2-P_1$

$⟹P_2=P_1+P$

$=\sqrt{2m\frac{K}{9}}+P$

$=\sqrt{\frac{2}{9}\frac{P^2}{2}}+P$

$=\frac{4P}{3}$