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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 36

  • question_answer
    A simple pendulum with a solid metal bob has a period T. The metal bob is now immersed in a liquid having density one-tenth that of the metal of the bob. The liquid is non-viscous. Now the period of the same pendulum with its bob remaining all the time in the liquid will be

    A) \[\frac{9}{10}T\]           

    B)        \[T\sqrt{\frac{10}{9}}\]

    C) Unchanged      

    D)        \[T\sqrt{\frac{9}{10}}\]

    Correct Answer: B

    Solution :

    [b] \[T=2\pi \sqrt{\frac{\ell }{g}}\] In a liquid \[T'=2\pi \sqrt{\frac{\ell }{g\left\{ 1-\frac{1}{\sigma } \right\}}}\] \[\sigma =\frac{density\,of\,bob}{density\text{ }of\text{ }liquid}\] \[\sigma =10\] \[T'=2\pi \sqrt{\frac{\ell }{g\left\{ 1-\frac{1}{10} \right\}}}\] \[=2\pi \sqrt{\frac{\ell }{g}}\sqrt{\frac{10}{9}}\] \[T'=T\sqrt{\frac{10}{9}}\]


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