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.
Answer & explanation
Correct answer: option 2
Time period of the pendulum
$=2 \pi \sqrt{\frac{\ell}{g_{\text {eff }}}}$
Here, $g_{\text {eff }}=\frac{\text { Tension in the string in equilibirium position }}{\text { mass of bob }}$
$=\frac{\sqrt{(mg)^2+(Eq)^2}}{m}$
$=\sqrt{g^2+(Eq / m)^2}$
∴ $T=2 \pi \sqrt{\frac{\ell}{\sqrt{g^2+(Eq / m)^2}}}$.