Question

A simple pendulum vibrates in a non- viscous liquid. The density of the liquid is p/8, where p is the density of the material of the bob. What is the time period if the time period of the pendulum in air is T.

Answer 1

As medium in non-viscous, damping is not present.

A bouyant force by liquid reduces apparent weight of bob.

In liquid,

$g^{\prime }=\frac{pg}{g^{\prime }}\Rightarrow$ where $p^{\prime }=p/8$

$=\frac{pg}{p/8}=8g$

as $T=2\pi \sqrt{\frac{2}{g}},\frac{T^{\prime }}{T}=\sqrt{\frac{g}{g^{\prime }}}=\sqrt{\frac{g}{8g}}\Rightarrow T^{\prime }=\frac{T}{2\sqrt{2}}$ (Reqd)