A homogenous rod of length $l=\eta x$ and mass M is lying on a smooth horizontal floor. A bullet of mass m hits the rod at a distance x from the middle of the rod at a velocity v₀ perpendicular to the rod and comes to rest after collision.  If the velocity of the farther end of the rod just after the impact is in the opposite direction of v₀, then 

 

A boy stands over the centre of a horizontal platform which is rotating freely with a speed of 2 revolutions/s about a vertical axis through the centre of the platform and straight up through the boy. He holds 2 kg masses in each of his hands close to his body. The. combined moment of inertia of the system is 1 kg$\times$metre². The boy now stretches his arms so as to hold the masses far from his body. In this situation, the moment of inertia of the system increases to 2kg$\times$metre². The kinetic energy of the system in the latter case as compared with that in the previous case will