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Work Power and Energy question

2024 · 6 Apr · Shift 1 · Q61
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Work Power and Energy question

2024 · 6 Apr · Shift 1 · Q61

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
A bullet of mass 50 g50 \mathrm{~g}50 g is fired with a speed 100 m/s100 \mathrm{~m} / \mathrm{s}100 m/s on a plywood and emerges with 40 m/s40 \mathrm{~m} / \mathrm{s}40 m/s. The percentage loss of kinetic energy is :
  1. A
    44%44 \%44%
  2. B
    16%16 \%16%
  3. C
    84%84 \%84%
  4. D
    32%32 \%32%
View written solutionFree

Correct answer: C

  1. Given data

    • Mass of bullet: m=50 g=0.05 kgm = 50\text{ g} = 0.05\text{ kg}m=50 g=0.05 kg
    • Initial speed: u=100 m/su = 100\text{ m/s}u=100 m/s
    • Final speed: v=40 m/sv = 40\text{ m/s}v=40 m/s
  2. Initial kinetic energy Ki=12mu2K_i = \frac{1}{2}mu^2Ki​=21​mu2 Ki=12(0.05)(100)2K_i = \frac{1}{2}(0.05)(100)^2Ki​=21​(0.05)(100)2 Ki=0.025×10000=250 JK_i = 0.025 \times 10000 = 250\text{ J}Ki​=0.025×10000=250 J

  3. Final kinetic energy Kf=12mv2K_f = \frac{1}{2}mv^2Kf​=21​mv2 Kf=12(0.05)(40)2K_f = \frac{1}{2}(0.05)(40)^2Kf​=21​(0.05)(40)2 Kf=0.025×1600=40 JK_f = 0.025 \times 1600 = 40\text{ J}Kf​=0.025×1600=40 J

  4. Loss in kinetic energy ΔK=Ki−Kf=250−40=210 J\Delta K = K_i - K_f = 250 - 40 = 210\text{ J}ΔK=Ki​−Kf​=250−40=210 J

  5. Percentage loss of kinetic energy % loss=ΔKKi×100\%\text{ loss} = \frac{\Delta K}{K_i} \times 100% loss=Ki​ΔK​×100 % loss=210250×100=84%\%\text{ loss} = \frac{210}{250} \times 100 = 84\%% loss=250210​×100=84%

  6. Option check

    • A: 44%44\%44% ❌
    • B: 16%16\%16% ❌
    • C: 84%84\%84% ✅
    • D: 32%32\%32% ❌

Therefore, the correct answer is Option C.

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