A uniform rod of mass 200 grams and length L = 1m is initially at rest in vertical position. The rod is hinged at centre such that it can rotate freely without friction about a fixed horizontal axis passing through its centre. Two particles of mass m = 100 grams each having horizontal velocity of equal magnitude u = 6 m/s strike the rod at top and bottom simultaneously as shown and stick to the rod. Find the angular speed (in rad/sec.) of rod when it becomes horizontal.

Explanation

From conservation of angular momentum
`m u L/2+m u L/2=[2m (L^(2))/12 +m(L/2)^(2)+(L/2)^(2)]omega`
`m u L=[(mL^(2))/6+(mL^(2))/4+(mL^(2))/4] omega=(2mL^(2))/3 omega ` or `omega=(3u)/(2L)=(3xx6)/(2xx1) = 9 rad//sec`