Answer to Question #49103 in Mechanics | Relativity for abdul wahab

Question

5. Two slender uniform bars, each of mass M and length L, meet at right angles at their midpoints to form a
rigid assembly that’s able to rotate freely about an axis through the intersection point, perpendicular to the
page. Attached to each end of each rod is a solid ball of clay of mass m. A bullet of mass mb is shot with
velocity v as shown in the figure (which is a view from above of the assembly) and becomes embedded in
the target clay ball.
(a) Show that the moment of inertia of each slender rod about the given rotation axis, not including the clay
balls, is ML2/ 12.
(b) Determine the angular velocity of the assembly after the bullet has become lodged in the targeted clay
ball.
(c) What is the resulting linear speed of each clay ball?
(d) Determine the ratio of the final KE of the assembly to the KE of the bullet before the impact.