Question

An object of weight W and density $\rho$ is dipped in a fluid of density ${\rho }_1$. Its apparent weight will be

• A. $W(\rho -{\rho }_1)$
• B. $W(1-\frac{{\rho }_1}{\rho })$
• C. $\left(\frac{\rho -{\rho }_1}{W}\right)$
• D. $W({\rho }_1-\rho )$

Answer 1

The correct option is B

$W(1-\frac{{\rho }_1}{\rho })$

Let $V$ be the volume of the body.
So, $W=\rho Vg$
Now, buoyant force, $B={\rho }_{1}Vg$
Apparent weight $=W-B=(\rho -{\rho }_1)Vg=(1-\frac{{\rho }_1}{\rho })W$