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

Question

Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiflhess K is T, when block is uncharged. If 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

Tardigrade Admin · Accepted Answer

The forces that act on the block are qE and mg. Since, qE and mg are constant forces, the only variable elastic force changes by kx (where, x is the elongation in the spring). Unbalanced (restoring) force, F=-kx ⇒ -mω 2x=-kx ⇒ ω =√(k/m)=T

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

T

$> T$

$< T$

$\geq T$

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

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

T

>T

<T

≥T

The forces that act on the block are qE and mg. Since, qE and mg are constant forces, the only variable elastic force changes by kx (where, x is the elongation in the spring). Unbalanced (restoring) force, F=−kx ⇒ −mω2x=−kx ⇒ ω=mk​​=T

$> T$

$< T$

$\geq T$