1. A system consists of a ball of mass M2 and a uniform rod of mass M1 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. The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves horizontally to the right. Express all answers in terms of Ml, M2, omega, d, and fundamental constants.

A. Derive an expression for the angular momentum of the rod about point P before the collision.

B. Derive an expression for the speed v of the ball after the collision.

C. Assuming that this collision is elastic, calculate the numerical value of the ratio M1/M2.

D. A new ball with the same mass M1 as the rod is now placed a distance x from the pivot. Again assuming that the collision is elastic, for what value of x will the rod stop moving after hitting the ball?