Question

A solid weighs $30\text{gf}$ in air and $26\text{gf}$ in water. Find the weight of solid in a liquid of density $0.6{\text{g/cm}}^3$.

• A. $28.4\text{kgf}$
• B. $28.6\text{kgf}$
• C. $28.2\text{kgf}$
• D. $28.8\text{kgf}$

Answer 1

The correct option is C $28.2\text{kgf}$

Given;
Weight of the solid in air ${\text{W}}_1$ = $30\text{gf}$

Weight of the solid immersed completely in water ${\text{W}}_2$ = $26\text{gf}$

Density of the liquid = $0.9{\text{g/cm}}^3$

R.D. of solid is given by : $⟹\frac{\text{Weight of substance in air}}{\text{Weight of body in air}-\text{Weight of body in liquid}}$

$⟹\frac{30}{30-26}=10$
$⟹$Now we have to find weight of liquid in liquid of density $0.6{\text{g/cm}}^3$
$⟹$ Let ${\text{W}}_3$ be the weight of solid in liquid
R.D. of solid is given by : $⟹\frac{{\text{W}}_3}{{\text{W}}_1-{\text{W}}_3}\times \text{relative density of water}$

$⟹$ $10$ = $\frac{30}{30-{\text{W}}_3}\times 0.6$
$⟹$${\text{W}}_3$ = $28.2\text{kgf}$
$\therefore$ Weight of solid in a liquid of density $0.6{\text{g/cm}}^3$ is $28.2\text{kgf}$