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MGIMS WARDHA MGIMS WARDHA Solved Paper-2009

  • question_answer
    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)  0.1%                                    

    B)  0.2%

    C)  0.3%                                    

    D)   0.4%

    Correct Answer: D

    Solution :

                     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 \[=2\alpha \Delta T\] \[=2\times {{10}^{-5}}\times 200\] \[=4\times {{10}^{-3}}=0.4%\]


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