A solid cube ABCD of side a and mass M is placed on a rough horizontal surface. A bullet of mass m and speed v is shot at the top of the cube so that cube rotates about
point D. The bullet sticks to the cube, m << M. Find the angular velocity of the cube.

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