A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v . The bullet emerges out of the bob with a speed v 3 and the bob just completes the vertical circle. The value of v is _____ m s - 1 (if g = 10 m s - 2 ).

Step-by-step solution

For the bob to completer the vertical circle, v b = 5 g l . From the conservation of momentum, m 1 v = m 2 v b + m 1 v 3 ⇒ 75 v = 50 5 g l + 75 v 3 ⇒ 75 2 v 3 = 50 5 × 10 × 2 ⇒ 75 2 v 3 = 50 × 10 ⇒ v = 500 × 3 150 = 500 50 = 10   m   s - 1