A simple pendulum has a time period T in air. | vedclass

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(D) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$.This implies $T \propto \frac{1}{\sqrt{g}}$.When the bob is immerse

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$\sqrt{\frac{8}{7}} T$

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(D) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$.This implies $T \propto \frac{1}{\sqrt{g}}$.When the bob is immersed in a liquid,the effective acceleration due to gravity $g'$ changes due to the buoyant force.The effective weight $W' = V \rho g - V \sigma g$,where $\rho$ is the density of the bob and $\sigma$ is the density of the liquid.Given $\sigma = \frac{\rho}{8}$,the effective acceleration $g'$ is:$g' = g \left(1 - \frac{\sigma}{\rho}\right) = g \left(1 - \frac{1}{8}\right) = g \left(\frac{7}{8}\right)$.The new time period $T'$ is given by:$T' = 2\pi \sqrt{\frac{l}{g'}} = 2\pi \sqrt{\frac{l}{g(7/8)}} = \sqrt{\frac{8}{7}} \left(2\pi \sqrt{\frac{l}{g}}\right) = \sqrt{\frac{8}{7}} T$.

$A$ simple pendulum has a time period $T$ in air. Its time period when it is completely immersed in a liquid of density one-eighth the density of the material of the bob is:

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