Question

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\left(\frac{4}{3}\right)\times1000\,kg/m^{3}.$ What relationship between $t$ and $t_0$ is true?

• A. $t = t_0$
• B. $t = t_0/2$
• C. $t = 2t_0$
• D. $t = 4t_0$

Answer 1

Answer: (C)

$t = 2t_0$

Answer 2

$\frac{T}{T_{0}} = \sqrt{\frac{1}{\left(1-\frac{\rho'}{\rho}\right)}} = \sqrt{\frac{1}{1-\frac{1}{3}}}$ $\Rightarrow \frac{T}{T_{0}} = 2$ or, $T = 2T_{0}$