Rotational Dynamics

A system consists of a ball of mass ##M_2## and a uniform rod of mass ##M_1## and length ##d##. The rod is attached to a horizontal frictionless table by a pivot at point ##P## and initially rotates at an angular speed ##\omega##, pictured below on the left. The rotational inertia of the rod about point ##P## is ##\frac{1}{3}M_1d^2## . The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves in the direction shown on the right. Express all answers in terms of ##M_1## , ##M_2## , ##\omega## , ##d## , and fundamental constants.
D. A new ball with the same mass ##M_1## as the rod is now placed a distance ##x## from the pivot, as shown above. Again assuming the collision is elastic, for what value ##x## will the rod stop moving after hitting the ball?