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Bullet gets embedded in a hanging block or bob: height risen or kinetic energy lost

This type of question, asked 3 times: 2021 Paper 6, 25 Jul 2022, 1 Feb 2024. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 6

    2
    A large block of wood of mass M=5.99 kgM = 5.99\text{ }kg is hanging from two long massless cords. A bullet of mass m=10 gm = 10\text{ }g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h=9.8 cmh = 9.8\text{ }cm before the pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take g=9.8 ms−2g = 9.8\ ms^{-2})

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  2. Question 2

    25 Jul 2022

    107
    A bag of sand of mass 9.8 kg9.8\text{ }kg is suspended by a rope. A bullet of 200 g200\text{ }g travelling with speed 10 ms−110{\text{ }ms}^{- 1} gets embedded in it, then loss of kinetic energy will be

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  3. Question 3

    1 Feb 2024

    16
    A simple pendulum of length 1 m1\text{ }m has a wooden bob of mass 1 kg1\text{ }kg. It is struck by a bullet of mass 10−2 kg10^{- 2}\text{ }kg moving with a speed of 2×102 ms−12 \times10^{2}{\text{ }ms}^{- 1}. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g=10 m/s2g = 10\text{ }m/s^{2} )

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