Q. 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 charges to $T.$ The ratio $T/T_{0}$ is equal to
A) $\left( \frac{g + \frac{qE}{m}}{g} \right)^{1/2}$
B) $\left( \frac{g}{g + \frac{qE}{m}} \right)^{3/2}$
C) $\left( \frac{g}{g + \frac{qE}{m}} \right)^{1/2}$
D) None of these
Explanation
(c) $T_{0} = 2\pi\sqrt{\frac{l}{g}}$
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Net downward force $mg^{''''''''} = mg + QE$
$\Rightarrow$ 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)}}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.