The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by
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(d) When the bob is immersed in water its effective weight = $\left( {mg - \frac{m}{\rho }g} \right) = mg\,\left( {\frac{{\rho - 1}}{\rho }} \right)$
$\therefore {g_{eff}} = g\,\left( {\frac{{\rho - 1}}{\rho }} \right)$
$\frac{{T'}}{T} = \sqrt {\frac{g}{{{g_{eff}}}}} $
$\frac{{T'}}{T} = \sqrt {\frac{\rho}{{\rho -1}}} $
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