Question

The time period of oscillation positively a charged spherical bob of a simple pendulum in a downward uniform electric field is.

• A. $T=2\pi \sqrt{\frac{l}{g}}$
• B. $T=2\pi \sqrt{\frac{l}{(g+\frac{Eq}{m})}}$
• C. $T=2\pi \sqrt{\frac{l}{(g-\frac{Eq}{m})}}$
• D. $T=2\pi \sqrt{\frac{l}{mg+Eq}}$

Answer 1

The correct option is B $T=2\pi \sqrt{\frac{l}{(g+\frac{Eq}{m})}}$



Time period of a simple pendulum, $T=2\pi \sqrt{\frac{l}{g}}$

In the presence of uniform electric field $g$ becomes $g_{eff}$

$g_{eff}=g+a$

$F_e=qEma=qEa=\frac{qE}{m}$

$\therefore g_{eff}=g+\frac{qE}{m}$

$\therefore$ Time period of the pendulum becomes,

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

$T=2\pi \sqrt{\frac{l}{g+\frac{Eq}{m}}}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (b) is the correct answer.