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A uniform rod of mass 20 kg and length 10 m is hinged at one end (A) and hangs vertically. A bullet of mass 5 kg moving horizontally at 10 m/s strikes the free end of the rod and embeds in it. Find the angular velocity of the rod immediately after the collision.
- 7/3 rad/s
- 3/7 rad/s
- 3/10 rad/s
- 3 rad/s
Correct answer: 3/7 rad/s
Solution
Angular momentum about A before collision: L = m*v*L = 5*10*10 = 500 kg.m²/s. Moment of inertia after: I = ML²/3 + mL² = 20*100/3 + 5*100 = 2000/3 + 500 = 3500/3 kg.m². omega = 500 / (3500/3) = 500*3/3500 = 1500/3500 = 3/7 rad/s.
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