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Q.

A spinning person when fold his hands his moment of inertia decreases by 25%. The kinetic energy increases by

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a

33.3%

b

12.5%

c

50%

d

17.3%

answer is B.

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Detailed Solution

$\begin{array}{l} K \cdot E = \frac{L^{2}}{2 I} \\ K \cdot E \propto \frac{1}{I} \\ \frac{K \cdot E_{1}}{K \cdot E_{2}} = \frac{I_{2}}{I_{1}} \\ \frac{K \cdot E_{1}}{K \cdot E_{2}} = \frac{75 %}{100 %} = \frac{3}{4} \\ \frac{ΔK \cdot E}{K \cdot E} = \frac{K \cdot E_{2} - K \cdot E_{1}}{K \cdot E_{1}} = \frac{4 - 3}{3} = \frac{1}{3} \\ = 0.333 = 33 \cdot 3 % \end{array}$

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