Question

A body weighs $50\text{g}$ in air and $40\text{g}$ when completely immersed in water. How much it will weigh when immersed completely in a liquid of relative density $1.5$?

• A. $30\text{g}$
• B. $35\text{g}$
• C. $45\text{g}$
• D. $25\text{g}$

Answer 1

The correct option is B $35\text{g}$

We know,
$\text{Upthrust on body in water}$ $=\text{Weight of body in air -Weight of body in water}$
$=(0.05-0.04)g\text{N}=0.01\times 10\text{N}$
$=0.1\text{N}$

We also know
Relative density of liquid
$=\frac{{\rho }_l}{{\rho }_w}$
$=\frac{\text{Upthrust on body in liquid}}{\text{Upthrust on body in water}}=1.5$
$=\frac{\text{Upthrust on body in liquid}}{0.1}=1.5$
$\Rightarrow \text{Upthrust on body in liquid}=0.15\text{N}$

Again,
$\text{Upthrust on body in liquid}$
$=\text{Weight of body in air -Weight of body in liquid}$
$\Rightarrow 0.15=0.5-W_l$
$\Rightarrow W_l=0.35\text{N}$
Mass, $m=\frac{0.35}{10}=0.035\text{kg}=35\text{g}$
$\therefore$ Body weighs as $35\text{g}$ in liquid.