Question

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

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

Answer 1

Answer: (D)

$2 \pi \sqrt{\frac{L}{\left(g- \frac{q\sigma}{ \varepsilon_{0 } m }\right)}}$

Answer 2