A small sphere carrying a charge ' $\mathrm{q}$ ' is hanging in between two parallel plates by a string of length $L$. Time period of pendulum is $\mathrm{T}_{0}$. When parallel plates are charged, the time period changes to $T$. The ratio $\mathrm{T} / \mathrm{T}_{0}$ is equal to

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Aicharya · Accepted Answer

$\mathrm{T}_{0}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$
When plates of the capacitor are charged, apart from weight, electric force due to the plates would also be acting on the charge particle in downward direction.

When the plates are charged, the net acceleration is, $g^{\prime}=g+a$
$T=2 \pi \sqrt{\frac{l}{g^{\prime}}}$ $\mathrm{g}^{\prime}=\mathrm{g}+\frac{\mathrm{q} \mathrm{E}}{\mathrm{m}} \quad\left(\mathrm{a}=\frac{\mathrm{q} \mathrm{E}}{\mathrm{m}}\right)$ $\therefore \quad \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}+\frac{\mathrm{q} \mathrm{E}}{\mathrm{m}}}}$ $\therefore \quad \frac{T}{T_{0}}=\left(\frac{g}{g+\frac{q E}{m}}\right)^{1 / 2}$

A small sphere carrying a charge ' $\mathrm{q}$ ' is hanging in between two parallel plates by a string of…

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