# A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is $T_0$. When parallel plates are charged, the time period changes to . The ratio $\frac{T}{}T_0$ is equal to Option 1) $\left ( \frac{g + \frac{qE}{m}}{g} \right )^{\frac{1}{2}}$ Option 2) $\left ( \frac{g} {g + \frac{qE}{m}}\right )^{\frac{3}{2}}$ Option 3) $\left ( \frac{g} {g + \frac{qE}{m}}\right )^{\frac{1}{2}}$ Option 4) None of these

V Vakul

As we have learnt

when electric field applied downward direction -

$\dpi{100} {T}'=2\pi \sqrt{\frac{l}{g+\frac{qE}{m}}}$

$\dpi{100} {T}'< T$

- wherein

Net downward force $mg' =mg + QE$
$\Rightarrow$Effect acceleration $\Rightarrow g' = \left (g + \frac{QE}{m} \right )$
Hence time period  $T = 2\pi \sqrt{\frac{l}{g}} = 2\pi \sqrt{\frac{l}{g + \frac{QE}{m}}}$

Option 1)

$\left ( \frac{g + \frac{qE}{m}}{g} \right )^{\frac{1}{2}}$

Option 2)

$\left ( \frac{g} {g + \frac{qE}{m}}\right )^{\frac{3}{2}}$

Option 3)

$\left ( \frac{g} {g + \frac{qE}{m}}\right )^{\frac{1}{2}}$

Option 4)

None of these

Exams
Articles
Questions