Question

The metallic Bob of simple pendulum has the relative density $\rho$. The time period of this pendulum is T. Is the metallic Bob is imerged in water then the new time period is

• A. $T\frac{\rho -1}{\rho }$
• B. $T\frac{\rho }{\rho -1}$
• C. $T\sqrt{\frac{\rho -1}{\rho }}$
• D. $T\sqrt{\frac{\rho }{\rho -1}}$

Answer 1

Answer: (D)

$T\sqrt{\frac{\rho }{\rho -1}}$

When the bob is immersed in water its effective weight

$W_{effective}=(mg-\frac{m}{\rho }g)$

$=mg\left(\frac{\rho -1}{\rho }\right)$

So, the effectiove value of acceleration due to gravity will be:

$\therefore geff=g\left(\frac{\rho -1}{\rho }\right)$

So, the ratio of the time periods can be given as:

$\frac{T^{{}^{\prime }}}{T}=\sqrt{\frac{g}{geff}}$

$\Rightarrow T^{{}^{\prime }}=T\sqrt{\frac{\rho }{\rho -1}}$