Question

A body of volume v and density d is completely immersed in a liquid of density $\rho$, then the apparent weight of the body will be

• A. vdg
• B. $v\rho g$
• C. $v(\rho -d)g$
• D. $v(d-\rho )g$

Answer 1

The correct option is D $v(d-\rho )g$

Buoyant force acting on the body is
$F_b=(\text{Volume of the displaced liquid}\times (\text{Density of the liquid})\times g$
$=\text{Volume of the body}\times \rho \times g$
= $\left(V\right)\left(\rho \right)\times g=\rho Vg$

Weight of the body.
$W=\text{Density of body}\times volume\times g$
$=\left(d\right)\left(V\right)\left(g\right)=dVg$
$\therefore$ Apparent weight of the body
$w^{\prime }=w-F_b=dVg-\rho Vg$
= $V(d-\rho )g$