Question

A simple pendulum has time period $T$. The pendulum is completely immersed in a non-viscous liquid whose density is one-tenth, of that of the material of the bob. The time period of the pendulum immersed in liquid is

• A. $ T $
• B. $ \sqrt{\frac{9}{10}}T $
• C. $ \sqrt{\frac{10}{9}T} $
• D. $ \frac{T}{10} $

Answer 1

Answer: (C)

Net weight of pendulum equals
$w=w-w_{t h}$
$\Rightarrow w=V \rho g-\frac{V \rho g}{10} $
$\Rightarrow w=\frac{9}{10} w$
$\Rightarrow w=\frac{9}{10} m g $
$(\because w=m g)$
$\Rightarrow g=\frac{9}{10} g $
$\therefore T=2 \pi \sqrt{\frac{l}{g}} $
$\Rightarrow T \sqrt{\frac{10}{9}} T$