Question

A neutral pendulum oscillates in a uniform electric field as shown in the figure. If a positive charge is given to the pendulum, then its time period

• A. increases
• B. first increases and then decreases
• C. decreases
• D. remains constant

Answer 1

The correct option is A increases

If we give a positive charge $q$ to the pendulum, then the force experienced by it due to the presence of the electric field will be $qE$ in the same direction as the electric field.

So we can draw the free body diagram for the bob of the pendulum as shown.


We know , Time period $T$ of a pendulum is given by

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

$g_{\text{eff}}=g-\frac{qE}{m}$

$T=2\pi \sqrt{\frac{l}{g-\frac{qE}{m}}}$

So as the denominator on the R.H.S decreases, $T$ will increase.

Hence, option (a) is the correct answer.