Q. The masses of five balls at rest and lying at equal distances in a straight line are in geometrical progression with ratio 2 and their coefficients of restitution are each 2/3. If the first ball be started towards the second with velocity $u$, then the velocity communicated to 5th ball is
A) $\frac{5}{9}u$
B) $\left( \frac{5}{9} \right)^{2}u$
C) $\left( \frac{5}{9} \right)^{3}u$
D) $\left( \frac{5}{9} \right)^{4}u$
Explanation
(d) We know that velocity of 2nd ball after collision is given by
$v_{2} = \frac{u_{1}(1 + e)m_{1}}{(m_{1} + m_{2})} + u_{2}\frac{(m_{2} - m_{1}e)}{(m_{1} + m_{2})}$
In present problem $u_{2} = 0,m_{2} = 2m_{1}$ and $e = 2/3$, hence
$v_{2} = \frac{u\left( 1 + \frac{2}{3} \right)m_{1}}{(m_{1} + 2m_{1})} = \frac{5}{9}u$
As four exactly similar type of collisions are taking place successively, hence velocity communicated to fifth ball
$v_{5} = \left( \frac{5}{9} \right)^{4}u$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.