# A simple pendulum has a time period T in vacuum. Its time period when it is completely immersed in a liquid…

Q: A simple pendulum has a time period T in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is

(a) $\displaystyle \sqrt{\frac{7}{8}} T$

(b) $\displaystyle \sqrt{\frac{5}{8}} T$

(c) $\displaystyle \sqrt{\frac{3}{8}} T$

(d) $\displaystyle \sqrt{\frac{8}{7}} T$

Ans: (d)

$\displaystyle T = 2\pi \sqrt{\frac{l}{g}}$

In a liquid ;

$\displaystyle T’ = 2\pi \sqrt{\frac{l}{g(1-\frac{\rho}{\sigma})}}$

Where ρ = density of liquid
and σ = density of solid

$\displaystyle T’ = 2\pi \sqrt{\frac{l}{g(1-\frac{\sigma /8}{\sigma})}}$

$\displaystyle T’ = 2\pi \sqrt{\frac{l}{g(1- \frac{1}{8})}}$

$\displaystyle T’ = 2\pi \sqrt{\frac{l}{g}.\frac{8}{7}}$

$\displaystyle = \sqrt{\frac{8}{7}} T$