Question

Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $K$ and is $T$, when block is uncharged. It a charge $q$ is given to the block then, the new time period of oscillation will be

• A. $T$
• B. $>T$
• C. $<T$
• D. $\ge T$

Answer 1

The correct option is A $T$

The forces that act on the block are $qE$ and $mg$. Since, $qE$ and $mg$ are constant forces, the only variable elastic forces changes by $kx$ (where $x$ is the elongation in the spring)
Unbalanced (restoring ) force, $F=-kx$
$\Rightarrow -m{\omega }^{2}x=-kx$
$\Rightarrow \omega =\sqrt{\frac{k}{m}}=T$