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
$w=w-w_{th}$
$\Rightarrow w=V\rho g-\frac{V\rho g}{10}$
$\Rightarrow w=\frac{9}{10}w$
$\Rightarrow w=\frac{9}{10}mg$
$(\because w=mg)$
$\Rightarrow g=\frac{9}{10}g$
$\therefore T=2\pi \sqrt{\frac{l}{g}}$
$\Rightarrow T\sqrt{\frac{10}{9}}T$