A simple pendulum oscillating in air has period $T.$ The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac {1}{16}$ of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is
JEE MAIN 2019, Diffcult
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For a simple pendulum $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}_{\mathrm{err}}}}$
Situation $1$: when pendulum is in air $\rightarrow g_{\text {eff }}=g$
Situation $2$ :when pendulum is in liquid
$\rightarrow g_{e f}=g\left(1-\frac{\rho_{\text {liquid }}}{\rho_{\text {body }}}\right)=g\left(1-\frac{1}{16}\right)=\frac{15 g}{16}$
So, $\frac{\mathrm{T}^{\prime}}{\mathrm{T}}=\frac{2 \pi \sqrt{\frac{\mathrm{L}}{15 \mathrm{g} / 16}}}{2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}}$
$\Rightarrow \mathrm{T}^{\prime}=\frac{4 \mathrm{T}}{\sqrt{15}}$
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