Question

A metallic solid sphere is rotating about its diameter as axes of rotation. If the temperature is increased by 200?C, the percentage increase in its moment of inertia is (Coefficient of linear expansion of the metal $ ={{10}^{-5}}{{/}^{o}}C $ )

• A. 0.001
• B. 0.002
• C. 0.003
• D. 0.004

Answer 1

The Correct Option is D

Moment of inertia $ (I)=\frac{2}{5}M{{R}^{2}} $ $ \Rightarrow $ $ \Delta I=\frac{2}{5}M2R\Delta R $ $ \therefore $ $ \frac{\Delta I}{I}=2\frac{\Delta R}{R}=2\alpha \Delta T $ $ \therefore $ Percentage increase in moment of inertia $ =2\alpha \Delta T $ $ =2\times {{10}^{-5}}\times 200 $ $ =4\times {{10}^{-3}}=0.4% $