Question

A simple pendulum of length $L$ is placed between the plates of a parallel plate capacitor having electric field $E$, as shown in figure. Its bob has mass $m$ and charge $q$. The time period of the pendulum is given by :

• A. $2\pi\sqrt{\frac{L}{\sqrt{g^{2}+\left(\frac{qE}{m}\right)^{2}}}} $
• B. $2\pi\sqrt{\frac{L}{\left(g+ \frac{qE}{m}\right)}}$
• C. $2\pi \sqrt{\frac{L}{\left(g- \frac{qE}{m}\right)}}$
• D. $2\pi \sqrt{\frac{L}{\sqrt{g^{2} - \frac{q^{2}E^{2}}{m^{2}}}}} $

Answer 1

Answer: (A)

$g_{eff } = \sqrt{g^{2} + \left(\frac{qE}{m}\right)^{2}} $
$T = 2\pi \sqrt{\frac{\ell}{g_{eff }}} $
$ = 2\pi \sqrt{\frac{\ell}{\sqrt{g^{2} +\left(\frac{qE}{m}\right)^{2}}}}$