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Bullet passes through or recoils from a pendulum bob that then just completes a vertical circle

This type of question, asked 2 times: 2021 Paper 21, 27 Jun 2022. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 21

    26
    A bullet of 10 g10\text{ }g, moving with velocity vv, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s100\text{ }m/s. The length of the pendulum is 0.5 m0.5\text{ }m and mass of the bob is 1 kg1\text{ }kg. The minimum value of vv, so that the pendulum describes a circle, is ____\_\_\_\_ m/sm/s. (Assume the string to be inextensible and g=10 m/s2g = 10\text{ }m/s^{2} )

  2. Question 2

    27 Jun 2022

    30
    A pendulum of length 2 m2\text{ }m consists of a wooden bob of mass 50 g50\text{ }g. A bullet of mass 75 g75\text{ }g is fired towards the stationary bob with a speed vv. The bullet emerges out of the bob with a speed v3\frac{v}{3} and the bob just completes the vertical circle. The value of vv is ____\_\_\_\_ ms−1ms^{- 1}. (if g=10 m/s2g = 10\text{ }m/s^{2} )