A simple pendulum of mass m and length $\ell$ carries a charge q. Find its time period when it is suspended in a uniform electric field region as shown in figure.

$T=2 \pi \sqrt{\frac{\ell}{\sqrt{g^2+(Eq / m)^2}}}$

Time period of the pendulum

$=2 \pi \sqrt{\frac{\ell}{g_{\text {eff }}}}$

Here, $g_{\text {eff }}=\frac{\text { Tension in the string in equilibirium position }}{\text { mass of bob }}$

$=\frac{\sqrt{(mg)^2+(Eq)^2}}{m}$

$=\sqrt{g^2+(Eq / m)^2}$

∴ $T=2 \pi \sqrt{\frac{\ell}{\sqrt{g^2+(Eq / m)^2}}}$.