Question

A piece of solid weighs $120\text{g}$ in air and $80\text{g}$ when completely immersed in water. The relative density of solid is

• A. $\frac{3}{2}$
• B. $\frac{4}{3}$
• C. $3$
• D. $2$

Answer 1

The correct option is C $3$

Let volume of solid is $V$
We know,
Relative density, $S=\frac{\text{Density of body}\left({\rho }_b\right)}{\text{Density of water}\left({\rho }_w\right)}$

$S=\frac{{\rho }_b\times V\times g}{{\rho }_w\times V\times g}$

$S=\frac{\text{Weight of body in air}}{\text{Weight of equal volume of water}}$

$S=\frac{\text{Weight of body in air}}{\text{Loss in weight in water}}$

$S=\frac{\text{Weight of body in air}\left(W_o\right)}{\text{Weight in air}\left(W_o\right)-\text{Weight in water}\left(W_w\right)}$

$S=\frac{W_o}{W_o-W_w}=\frac{120}{120-80}=3$