Question

The bob of a pendulum of mass 'm', suspended by an inextensible string of length 'L' as shown in the figure carried small charge 'a'. An infinite horizontal plane conductor with uniform surface charge density ${}^{\prime }{\sigma }^{\prime }$, is placed below it. What will be the time period of the pendulum for small amplitude oscillations.

• A. $2\pi \sqrt{\frac{L}{(g-\frac{mq}{{\epsilon }_0\sigma })}}$
• B. $\sqrt{\frac{L}{\left(g-\frac{mq\sigma }{{\epsilon }_0}\right)}}$
• C. $\frac{1}{2\pi }\sqrt{\frac{L}{(g-\frac{q\sigma }{{\epsilon }_{0}m})}}$
• D. $2\pi \sqrt{\frac{L}{(g-\frac{q\sigma }{{\epsilon }_{0}m})}}$

Answer 1

The correct option is D $2\pi \sqrt{\frac{L}{(g-\frac{q\sigma }{{\epsilon }_{0}m})}}$

$TP=2\pi \sqrt{\frac{L}{g-\frac{qE}{m}}}$
$=2\pi \sqrt{\frac{L}{g-\frac{q\sigma }{{\epsilon }_0\left(m\right)}}}$.