A rigid uniform rod of mass M and length L is placed along the Y-axis on a smooth horizontal surface with its centre at the origin. Two particles , each of mas `m ( = M //12) ` hits simultaneously , at the two ends with equal speed v as shown in the figure. The collision is completely inelastic.
(i) Find the angular velocity of the system after the collision.
(ii) Two particles of mass 2m and m are placed respectively at ( `L//2, 0)` and `( - L//2, 0)`. Calculate the time when the rod hits these particles.

Answer

(a) `( 2v)/( 3L) `, ( b) `( 3 pi L )/( 4 v )`