Question

A simple pendulum has a length $l\&$ mass of bob $m.$ the bob is given a charge $q$ coulomb. The pendulum is suspended in a uniform horizontal electric field of strength $E$ as shown in figure, then calculate the time period of oscillation when the bob is slightly displaced from its mean position.

• A. $2\pi \sqrt{\frac{l}{g}}$
• B. $2\pi \sqrt{\left\{\frac{l}{g+\frac{qE}{m}}\right\}}$
• C. $2\pi \sqrt{\left\{\frac{l}{g-\frac{qE}{m}}\right\}}$
• D. $2\pi \sqrt{\frac{l}{g^2+{\left(\frac{qE}{m}\right)}^2}}$

Answer 1

The correct option is D $2\pi \sqrt{\frac{l}{g^2+{\left(\frac{qE}{m}\right)}^2}}$

length $=l$ and mass $=m$ bob charge $=q$

field strength $=F$

$T=2\pi \sqrt{\frac{l}{g^2+{\left(\frac{qE}{m}\right)}^2}}$

$qE=\frac{1}{2}{mV}^2$

or, $V={\left(\frac{qE}{m}\right)}^2$