Question 21

A bullet of 10 g, moving with velocity $$v$$, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m s$$^{-1}$$. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of $$v$$ in m s$$^{-1}$$, so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m s$$^{-2}$$)

Correct Answer: 400

Required velocity of the bob immediately after collision:

$$v_b = \sqrt{5gL} = \sqrt{5 \times 10 \times 0.5} = 5\text{ m s}^{-1}$$

Using conservation of linear momentum: $$m v = m v' + M v_b$$

$$0.01v = 0.01(-100) + 1(5)$$

$$0.01v = -1 + 5 \implies 0.01v = 4 \implies v = 400\text{ m s}^{-1}$$

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