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MHT CET 2024 (10 May, Shift 1) · Conservation of Energy

Conservation of Energy question from MHT CET 2024 (10 May, Shift 1)

Q14MHT CET 2024 · 10 MAY · SHIFT 1Medium

Conservation of Energy

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

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Answer: (a)

  1. Heat produced =75%= 75\% of KE: Q=34⋅12mV2Q = \frac{3}{4} \cdot \frac{1}{2}mV^2 (in joule).
  2. In calories Q=3mV28JQ = \frac{3mV^2}{8J}, and Q=ms ΔTQ = ms\,\Delta T.
  3. ms ΔT=3mV28J⇒ΔT=3V28Jsms\,\Delta T = \frac{3mV^2}{8J} \Rightarrow \Delta T = \frac{3V^2}{8Js}
  4. So the answer is (a).
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