Find out the velocity of the bullet:
A bullet of weight W1 = 5 N is fired into a body B2 of weight W2 = 45 N suspended by a string of length L = 1 metres. Because of impact, body B2 swings through an ∠ θ = 60o. If the impact is fully plastic, find out the velocity of the bullet.
Refer Figure. Let initial velocity of the bullet by V1.
Initial velocity of B2 = V2 = 0
After impact, we have, by principle of conservation of momentum
(m1 + m2) VC = m1 V1 --------- (I)
By using principle of conservation of energy for the second event when body B2 swings through a maximum ∠ θ = 60o,
((W1 + W2) /2 g)(Vc) 2 = (W1 + W2) × L × (1 - cosθ)
∴ V 2 = 2 g L (1/2) = 9.8 × 1
∴ Vc = 3.13 m / sec .