Q. Three identical sphere lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is $L$. The first sphere is moved with a velocity $u$ towards the second sphere at time $t = 0$. The coefficient of restitution for collision between any two blocks is 1/3. Then choose the correct statement
A) The third sphere will start moving at $t = \frac{5L}{2u}$
B) The third sphere will start moving at $t = \frac{4L}{u}$
C) The centre of mass of the system will have a final speed $u/3$
D) The centre of mass of the system will have a final speed $u$
Explanation
(a) First sphere will take a time $t_{1}$, to start motion in second sphere on colliding with it, where $t_{1} = \frac{L}{u}$
Now speed of second sphere will be
$v_{2} = \frac{u}{2}(1 + e) = \frac{2}{3}u$
Hence time taken by second sphere to start motion in third sphere $t_{2} = \frac{L}{2/3u} = \frac{3L}{2u}$
$\therefore$ Total time $t = t_{1} + t_{2} = \frac{L}{u} + \frac{3L}{2u} = \frac{5L}{2u}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.