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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        When the temperature of a rod increases from t to\[t+\Delta t,\]its moment of inertia increases from \[I\]to\[I+\Delta I\].If\[\alpha \]be the coefficient of linear expansion of the rod, then the value of\[\frac{\Delta I}{I}\]is

    A)  \[2\alpha \,\Delta t\]                    

    B)  \[\alpha \,\Delta t\]

    C)  \[\frac{\alpha \,\Delta t}{2}\]                   

    D)  \[\frac{\,\Delta t}{\alpha }\]

    Correct Answer: A

    Solution :

                    Moment of inertia of a rod \[I=\frac{M{{\lambda }^{2}}}{12}\] \[dI=\frac{M}{12}2\lambda \,d\lambda \] \[\frac{dI}{I}=2\frac{d\lambda }{\lambda }=2\alpha \Delta t\]


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