Question

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 :

• A. $4T\sqrt{\frac{1}{15}}$
• B. $2T\sqrt{\frac{1}{10}}$
• C. $4T\sqrt{\frac{1}{14}}$
• D. $2T\sqrt{\frac{1}{14}}$

Answer 1

Answer: (A)

For a simple pendulum T = $2\pi \sqrt{\frac{L}{g_{eff}}}$
situation 1 : when pendulum is in air $\to g_{ef}$f = g
situation 2 : when pendulum is in liquid
$\to g_{eff}=g(1-\frac{{\rho }_{liquid}}{{\rho }_{body}})=g(1-\frac{1}{16})=\frac{15g}{16}$
$So,\frac{T^{\prime }}{T}=\frac{2\pi \sqrt{\frac{L}{15g/16}}}{2\pi \sqrt{\frac{L}{g}}}\Rightarrow T^{\prime }=\frac{4T}{\sqrt{15}}$
Option (1)