Question

A solid body weighs $2.1\text{N}$ in air and has a relative density of $8.4$. How much will it weigh in a liquid of relative density $1.8$?

• A. $1.75\text{N}$
• B. $1.7\text{N}$
• C. $1.65\text{N}$
• D. $1.6\text{N}$

Answer 1

The correct option is C $1.65\text{N}$

Weight of the body in air $\left(W_1\right)=2.1\text{N}$
Relative density of the body $=8.4$
Weight of the body in water $=W_2$
Relative density $=\frac{W_1}{W_1-W_2}$
$W_2=1.85\text{N}$
Upthrust $=W_1–W_2$
Upthrust $=0.25\text{N}$
Upthrust due to liquid = Upthrust due to water $\times$ Relative density of liquid
Upthrust due to liquid $=0.25\times 1.8=0.45\text{N}$
Weight of the body in liquid = True weight – Upthrust due to liquid
Weight of the body in liquid $=2.1–0.45=1.65\text{N}$