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 $$\cfrac{1}{16}$$th of material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

Answer 1

Correct option is A. $$4T\sqrt { \cfrac { 1 }{ 15 } } $$
For simple pendulum $$T=2\pi \sqrt { \cfrac { L }{ { g }_{ eff } } } $$
situation 1:when pendulum is in air $$\rightarrow { g }_{ eff }=g\left( 1-\cfrac { { \rho }_{ liquid } }{ { \rho }_{ body } } \right) =g\left( 1-\cfrac { 1 }{ 16 } \right) =\cfrac { 15g }{ 16 } $$
so, $$\cfrac { T' }{ T } =\cfrac { 2\pi \sqrt { \cfrac { L }{ 15g/16 } } }{ 2\pi \sqrt { \cfrac { L }{ g } } } \Rightarrow T'=\cfrac { 4T }{ \sqrt { 15 } } $$