Q. The fraction of a floating object of volume $V_{0}$ and density $d_{0}$ above the surface of a liquid of density $d$ will be
A) $\frac{d_{0}}{d}$
B) $\frac{dd_{0}}{d + d_{0}}$
C) $\frac{d - d_{0}}{d}$
D) $\frac{dd_{0}}{d - d_{0}}$
Explanation
(c) For the floatation $V_{0}d_{0}g = V_{in}\ d\ g \Rightarrow V_{in} = V_{0}\frac{d_{0}}{d}$
$\therefore V_{out} = V_{0} - V_{in} = V_{0} - V_{0}\frac{d_{0}}{d} = V_{0}\left\lbrack \frac{d - d_{0}}{d} \right\rbrack$
$\Rightarrow \frac{V_{out}}{V_{0}} = \frac{d - d_{0}}{d}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.