Q. A body of density $d_{1}$ is counterpoised by $Mg$ of weights of density $d_{2}$ in air of density $d$. Then the true mass of the body is
A) $M$
B) $M\left( 1 - \frac{d}{d_{2}} \right)$
C) $M\left( 1 - \frac{d}{d_{1}} \right)$
D) $\frac{M(1 - d/d_{2})}{(1 - d/d_{1})}$
Explanation
(d) Let $M_{0} =$ mass of body in vacuum
Apparent weight of the body in air = Apparent weight of standard weight in air
$\Rightarrow$ Actual weight – upthrust due to displaced air
$\Rightarrow M_{0}g - \left( \frac{M_{0}}{d_{1}} \right)dg = Mg - \left( \frac{M}{d_{2}} \right)dg \Rightarrow M_{0} = \frac{M\left\lbrack 1 - \frac{d}{d_{2}} \right\rbrack}{\left\lbrack 1 - \frac{d}{d_{1}} \right\rbrack}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.