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  4. A thin circular metal disc of radius 500.0 mm is set rotating about a central axis normal to its plane. Upon raising its temperature gradually, the radius increases to 507.5 mm. The percentage change in the rotational kinetic energy will be

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Q. A thin circular metal disc of radius 500.0 mm is set rotating about a central axis normal to its plane. Upon raising its temperature gradually, the radius increases to 507.5 mm. The percentage change in the rotational kinetic energy will be

Thermal Properties of Matter

Solution:

Rotational $KE : K =\frac{ L ^{2}}{2 I }$ where $L$ is the angular momentum and $I$ is the moment of inertia. $L$ is conserved in the process and remains constant.
$
\frac{\Delta K }{ K }=-\frac{\Delta I }{ I }=-\left(\frac{(507.5)^{2}-(500)^{2}}{(500)^{2}}\right)=-0.03
$
$\therefore $ Percentage increase in KE: $-0.03 \times 100 \%=-3 \%$