Consider a uniform rod of mass M= 4m and length L  pivoted about its center. A mass m moving with velocity  $\nu$  making angle $\theta =\frac{\pi }{4}$  to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision 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