• # question_answer 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 $\frac{1}{16}$th 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 9-4-2019 Morning] A) $4T\sqrt{\frac{1}{15}}$B)   $2T\sqrt{\frac{1}{10}}$C) $4T\sqrt{\frac{1}{14}}$                   D) $2T\sqrt{\frac{1}{14}}$

For a simple pendulum $T=2\pi \sqrt{\frac{L}{{{g}_{eff}}}}$ situation 1 : when pendulum is in air $\to {{g}_{eff}}=g$ situation 2 : when pendulum is in liquid $\to {{g}_{eff}}=g\left( 1-\frac{{{\rho }_{liquid}}}{{{\rho }_{body}}} \right)=g\left( 1-\frac{1}{16} \right)=\frac{15g}{16}$ So,$\frac{T'}{T}=\frac{2\pi \sqrt{\frac{L}{15g/16}}}{2\pi \sqrt{\frac{L}{g}}}\Rightarrow T'=\frac{4T}{\sqrt{15}}$ Option [a]