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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    A torsional pendulum consists of a solid disc connected to a thin wire \[\alpha =2.4\times 10-5/{}^\circ C\]at its centre. Find the percentage change in the time period between peak winter \[\left( 5{}^\circ C \right)\]and peak summer\[\left( 45{}^\circ C \right)\].

    A) \[9.6\times {{10}^{-4}}%\]                   

    B) \[9.6\times {{10}^{-2}}%\]

    C) \[6.9\times {{10}^{-4}}%\]                   

    D) \[6.9\times {{10}^{-2}}%\]

    Correct Answer: B

    Solution :

    Time period  of torsional pendulum \[T=2\pi \sqrt{\frac{1}{C}}\]
    \[\therefore \frac{\Delta T}{T}=-\frac{1}{2}\frac{\Delta I}{I}\]
    As \[I=k{{L}^{2}}\]
    \[\therefore \frac{\Delta I}{I}=\frac{2\Delta L}{L}\]
    Due to small change in temperature \[\Delta \]T,
    \[\Delta L=L\alpha \,\Delta T\]
    \[\therefore \frac{\Delta I}{I}=2\alpha \Delta T\]
    And \[\therefore \frac{\Delta T}{T}=\frac{1}{2}\times 2\alpha \Delta T\]
    =\[\alpha \Delta T=2.4\times {{10}^{-5}}\times (45-5)\] = \[9.6\times {{10}^{-4}}=9.6\times {{10}^{-2}}%\]


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