Question

A piece of solid weight $120g$ in air, $80g$ in water and $60g$ in a liquid. The relative density of the solid and that of the liquid are respectively

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

Answer 1

The correct option is D $3,\frac{3}{2}$

Given,

Weight of the body in air $=120g$

Weight of body in air $=80g$

Weight of body in liquid $=60g$

The relative density of an object is equal to the ratio of its weight in air and the difference in its weight in air and its weight when the object is submerged in liquid.

For relative density of solid $=\frac{120g}{120g-80g}=\frac{120}{40}=3$

Hence, the relative density of solid is $3$.

Now, relative density of liquid can be calculated as the ration of loss of weight of solid in liquid to the loss of weight in water.

Relative density of liquid $=\frac{60g}{120g-80g}=\frac{60}{40}=\frac{3}{2}$

Hence, the relative density of liquid is $\frac{3}{2}$.

The correct option is D.