Q- A uniform rod AB, of mass m and length 4a, is free to rotate in a vertical plane about a fixed horizontal axis through the point X on the rod, where AX = a. The rod is hanging at rest with B below A, when it is struck at its mid point by a particle of mass 3m moving horizontally with speed u in a direction perpendicular to the rod. Immediately after the impact P adheres to the rod.
(a) Show that after the impact the moment of inertia about the axis of the rod and particle together is 16ma²/3
(b) Find in terms of u and a, the angular speed of the rod immediately after the impact.

In the subsequent motion, the rod comes to instantaneous rest when it has rotated through an angle of 120⁰
(c) Find the velocity of the particle u.

When the rod comes to instantaneous rest, the force exerted by the axis on the rod is F. Find in terms of m and g, the magnitude of the component F which is
(d) parallel to the rod
(e) perpendicular to the rod

Solution: