Weight of the body in air = W_{1} gf

Weight of the body in liquid = W_{2} gf

Weight of the body in water = W_{3} gf

(i) Let V be the volume of the body.

Upthrust due to water = loss in weight when immersed in water = (W_{1} – W_{3}) gf **…[Eq 1]**

Weight of water displaced = Volume of water displaced × density of water × g

The volume of water displaced = Volume of the body = V

Density of water = 1 g cm^{-3}

∴ Weight of water displaced = V × 1 × g = V gf **…[Eq 2]**

But the weight of water displaced is equal to the upthrust due to water

∴ From eqns 1 & 2,

V = (W_{1} – W_{3}) cm^{3}

**∴ Volume of the body = V = (W _{1} – W_{3}) cm^{3}**

(ii) Upthrust due to liquid = loss in weight when immersed in liquid = (W_{1} – W_{2}) gf

(iii) **Relative density of the solid**

RD of solid = W_1\over W_1 - W_3

(iv) **Relative density of the liquid**

RD of liquid = W_1 - W_2\over W_1 - W_3