Question

Three identical spheres lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is $L$ . The first sphere is moving with a velocity $u$ towards the second sphere at time $t=0$ . The coefficient of restitution for a collision between any two blocks is $\frac{1}{3}$ . The correct statement is

• A. The third sphere will start moving at $t=\frac{5 L}{2 u}$
• B. The third sphere will start moving at $t=\frac{4 L}{u}$
• C. The centre of mass of the system will have a final speed $2u$
• D. The centre of mass of the system will have a final speed $u$

Answer 1

Answer: (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
$v_{2}=\frac{u}{2}\left(1 + e\right)=\frac{2}{3}u$
Hence, time taken by second sphere to start motion in third sphere
$\therefore $ Total time $t=t_{1}+t_{2}=\frac{L}{u}+\frac{3 L}{2 u}=\frac{5 L}{2 u}$