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  4. A simple pendulum has a length l and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by

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Q. A simple pendulum has a length $ l $ and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by

MGIMS WardhaMGIMS Wardha 2008

Solution:

Time period of simple pendulum in air
$ T=2\pi \sqrt{\frac{l}{g}} $ When it is suspended between vertical plates of a charged parallel plate capacitor, then acceleration due to electric field, $ a=\frac{qE}{m} $ This acceleration is acting horizontally and acceleration due to gravity is acting vertically. So, effective acceleration $ g'=\sqrt{{{g}^{2}}+{{a}^{2}}}=\sqrt{{{g}^{2}}+{{\left( \frac{qE}{m} \right)}^{2}}} $ Hence, $ T'=2\pi $ $ \sqrt{\frac{l}{\sqrt{{{g}^{2}}+{{\left( \frac{qE}{m} \right)}^{2}}}}} $

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