A girl of mass M stands on the rim of a frictionless merry go-round of radius R and rotational inertia I that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry go-round. The speed of the rock, relative to the ground, is v. Afterward, the linear speed of the girl is

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