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  4. 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

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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 bePhysics Question Image

Jharkhand CECEJharkhand CECE 2012

Solution:

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 $
$ \Rightarrow $ $ -m{{\omega }^{2}}x=-kx $
$ \Rightarrow $ $ \omega =\sqrt{\frac{k}{m}}=T $