An impulse J = mv at one end of a stationary uniform frictionless rod of mass m and length l which is free to rotate in a gravity-free space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through

J = mv = mv'⇒ Velocity of the CM of rod = vApplying impulse momentum equation about the CM of rodAbout instantaneous axis of rotation the rod is considered to have pure rotation.Let instantaneous axis of rotation be located at a distance x from the colliding end [Fig (b)]ωl2−vl−x=v+ωl2x      .......(i)Substituting the value of w = 6V/l in eq. (i), we get x=23l..