Three identical sphere lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is . The first sphere is moved with a velocity towards the second sphere at time . 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 
b) 
The third sphere will start moving at 
c) 
The centre of mass of the system will have a final speed 
d) 
The centre of mass of the system will have a final speed 

Three identical sphere lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is . The first sphere is moved with a velocity towards the second sphere at time . 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 
b) 
The third sphere will start moving at 
c) 
The centre of mass of the system will have a final speed 
d) 
The centre of mass of the system will have a final speed 

(a) First sphere will take a time , to start motion in second sphere on colliding with it, where Now speed of second sphere will be Hence time taken by second sphere to start motion in third sphere Total time 