A small sphere carrying a charge ‘$q$’ is hanging in between two parallel plates by a string of length $L$. Time period of pendulum is ${T_0}$. When parallel plates are charged, the time period changes to $T$. The ratio $T/{T_0}$ is equal to
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(c) Net downward force $mg' = mg + QE$
$==>$ Effect acceleration $g' = \left( {g + \frac{{QE}}{m}} \right)$
Hence time period $T = 2\pi \sqrt {\frac{l}{{g'}}} = 2\pi \sqrt {\frac{l}{{\left( {g + \frac{{QE}}{m}} \right)}}} $
$==>$ Effect acceleration $g' = \left( {g + \frac{{QE}}{m}} \right)$
Hence time period $T = 2\pi \sqrt {\frac{l}{{g'}}} = 2\pi \sqrt {\frac{l}{{\left( {g + \frac{{QE}}{m}} \right)}}} $
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