Work Energy Power

JEE Main level, single correct, medium

53 of 183

Question 53 of 183

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 :

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Answer: (A) 84%84 \%

Ki=12 m(100)2 Kf=12 m(40)2% loss =∣Kf−Ki∣Ki×100=∣12 m(40)2−12 m(100)2∣12 m(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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