An impulse at one end of a stationery uniform frictionless rod of mass and length which is free to rotate in a gravityfree space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through 

a) 
Its centre of mass 
b) 
The centre of mass of the rod plus ball 
c) 
The point of impact of the ball on the rod 
d) 
The point which is at a distance 2/3 from the striking end 
An impulse at one end of a stationery uniform frictionless rod of mass and length which is free to rotate in a gravityfree space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through 

a) 
Its centre of mass 
b) 
The centre of mass of the rod plus ball 
c) 
The point of impact of the ball on the rod 
d) 
The point which is at a distance 2/3 from the striking end 
(d)
Velocity of the CM of rod =
Applying impulse momentum equation about the CM of rod
About instantaneous axis of rotation the rod is considered to have pure rotation
Let instantaneous axis of rotation be located at a distance from the colliding end
…(i)
Substituting the value of in Eq.(i), we get