Q. The metallic bob of a simple pendulum has the relative density $\rho.$ The time period of this pendulum is $T.$ If the metallic bob is immersed in water, then the new time period is given by
A) $T\frac{\rho - 1}{\rho}$
B) $T\frac{\rho}{\rho - 1}$
C) $T\sqrt{\frac{\rho - 1}{\rho}}$
D) $T\sqrt{\frac{\rho}{\rho - 1}}$
Explanation
(d) When the bob is immersed in water its effective weight
$= \left( mg - \frac{m}{\rho}g \right) = mg\left( \frac{\rho - 1}{\rho} \right)$
$\therefore g_{eff} = g\left( \frac{\rho - 1}{\rho} \right)$
$\frac{T^{'}}{T} = \sqrt{\frac{g}{g_{eff}}} \Rightarrow T^{'} = T\sqrt{\frac{\rho}{(\rho - 1)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.