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JEE Main 20246 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Morning Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2024 · 6 April · Morning Shift · Physics · Work, Power and Energy

A bullet of mass 50 ~g is fired with a speed 100 ~m / s on a...

A bullet of mass 50 g50 \mathrm{~g} is fired with a speed 100 m/s100 \mathrm{~m} / \mathrm{s} on a plywood and emerges with 40 m/s40 \mathrm{~m} / \mathrm{s}. The percentage loss of kinetic energy is :

Options

  1. A84%84 \%
  2. B16%16 \%
  3. C32%32 \%
  4. D44%44 \%

Correct answer

A. 84%84 \%

Step-by-step solution

Ki=12m(100)2Kf=12m(40)2% loss =∣Kf−Ki∣Ki×100=∣12m(40)2−12m(100)2∣12m(100)2×100=∣1600−100×100∣100=84%\begin{aligned} \mathrm{K}_{\mathrm{i}} & =\frac{1}{2} \mathrm{ m}(100)^2 \\ \mathrm{ K}_{\mathrm{f}} & =\frac{1}{2} \mathrm{ m}(40)^2 \\ \% \text{ loss } & =\frac{\left|\mathrm{K}_{\mathrm{f}}-\mathrm{K}_{\mathrm{i}}\right|}{\mathrm{K}_{\mathrm{i}}} \times 100 \\ & =\frac{\left|\frac{1}{2} \mathrm{ m}(40)^2-\frac{1}{2} \mathrm{ m}(100)^2\right|}{\frac{1}{2} \mathrm{ m}(100)^2} \times 100 \\ & =\frac{|1600-100 \times 100|}{100}=84 \%\end{aligned}
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