NEET Sample Paper NEET Sample Test Paper-15

  • question_answer The bob of a simple pendulum is hanging vertically down from a fixed identical bob by means of a string of length\[l.\] If both bobs are charged with a charge q each, time period of the pendulum is: (ignore the radii of the bobs)

    A)  \[2\pi \sqrt{\frac{\ell }{g+\sqrt{\frac{{{q}^{2}}}{{{\ell }^{2}}m}}}}\]           

    B)  \[2\pi \sqrt{\frac{\ell }{g-\sqrt{\frac{{{q}^{2}}}{{{\ell }^{2}}m}}}}\]

    C) \[2\pi \sqrt{\frac{\ell }{g}}\]               

    D)  \[2\pi \sqrt{\frac{\ell }{g-\left( \frac{{{q}^{2}}}{\ell } \right)}}\]

    Correct Answer: C

    Solution :

    Charge on each bob = q \[\therefore \] force of repulsion between them \[=\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}{{\ell }^{2}}}.\] As this force is mutual, value of g is not affected. Time period remains the same. \[\therefore \]\[t=2\pi \sqrt{\frac{\ell }{g}}.\] Hence, the correction option is [c].

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