Question

The period of small oscillations of a pendulum, that is bob suspended by a thread L = 20 cm in length, if it is located in a liquid whose density is 3 times less than that of bob is $\frac{5+x}{10}$ second (approximately). Find the value of x. ___

Answer 1

$g_{eff}=\frac{Weight-Upthrust}{Mass}$
$=\frac{v\rho g-v\frac{\rho }{3}g}{v\rho }=\frac{2}{3}g$
$T=2\pi \sqrt{\frac{L}{g_{eff}}}=2\pi \sqrt{\frac{3L}{2g}}=2\pi \sqrt{\frac{3\times 0.2}{2\times 9.8}}$
$orT\simeq 1.1s=\frac{5+6}{10}s$
$\Rightarrow x=6$