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Lead bullet strikes a wall and stops: temperature rise when a fraction of its energy becomes heat

The same question, asked 3 times: 4 May 2023 S2*, 10 May 2023 S1*, 19 May 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S2

    20
    A lead bullet moving with velocity 'v' strikes a wall and stops. If 50% of its energy is converted into heat, then the increase in temperature is (s=s = specific heat of lead)

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  2. Question 2

    10 May 2023 S1

    18
    A lead bullet moving with velocity 'V' strikes a wall and stops. If 75% of its energy is converted into heat, then the increase in temperature is (s=s= specific heat of lead, J=J= mechanical equivalent of heat)

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  3. Question 3

    19 May 2026 S2

    104
    A lead bullet moving with velocity 'vv' strikes a wall and stops. 75%75\% of its energy is converted into heat. If the increase in the temperature is v2nJs\dfrac{v^2}{nJs}, then the value of nn is {s=specific heat of lead,J=mechanical equivalent of heat}\{s = \text{specific heat of lead}, J = \text{mechanical equivalent of heat}\}

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