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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical?

    A) \[60{}^\circ \]                   

    B) \[90{}^\circ \]

    C)  \[30{}^\circ \]                                  

    D) \[45{}^\circ \]

    Correct Answer: B

    Solution :

    In mean position,\[X=\overline{X+Y}\] Net force \[\overline{X+Y}=\overline{X}.\overline{Y}\] \[[k\,\,x]=\] \[k=\frac{1}{x}=\frac{1}{[L]}=[{{L}^{-1}}]\] Let maximum angular displacement with vertical be \[[k]=[{{L}^{-1}}]\]. Then, \[KE=\frac{1}{2}m{{v}^{2}}=kt\] \[\frac{1}{2}m.2v.\frac{dv}{dt}=k\] \[m\frac{dv}{dt}=\frac{k}{v}\]


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