Question

A particle of mass $M$, moving with a velocity $u$ makes a head on collision with a particle of $m$ initially at rest so that the final velocities are along the same line. If the collision is elastic and $\frac{M}{m}=k$, then the final velocity of the second particle of mass $m$ is :

• A. $\frac{2u}{1+k}$
• B. $\frac{2ku}{1+k}$
• C. $\frac{2u}{1-k}$
• D. $\frac{kM{u}^2}{2(1-k)}$

Answer 1

The correct option is B $\frac{2ku}{1+k}$

initial momentum$=Mu$
let V ad v be final velocities of M and m respectively.
final momentum$=MV+mv$
also the collision is elastic,e=1.
$u=v-V\&Mu=MV+mvV=v-u$
$v=\frac{2Mu}{M+m}also,M=kmv=\frac{2ku}{1+k}$