Q. A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is $T$. When the sphere is immersed in a non-viscous liquid of density $\frac{1}{10}$ that of brass, it will act as a simple pendulum of period
A) $T$
B) $\frac{10}{9}\ T$
C) $\sqrt{\left( \frac{9}{10} \right)}\ T$
D) $\sqrt{\left( \frac{10}{9} \right)}\ T$
Explanation
(d) $\frac{T'}{T} = \sqrt{\frac{g}{g'}} = \sqrt{\left\lbrack \frac{g}{g\left( 1 - \frac{1}{10} \right)} \right\rbrack} = \sqrt{\frac{10}{9}}$
$\Rightarrow$ $T^{'} = \sqrt{\frac{10}{9}}T$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.