A body weighs W gf in air and W₁ gf when it is completely immersed in water. Find (i) volume of the body, (ii) upthrust on the body, (iii) relative density of material of the body.

Given,

Weight of body in air = W

Weight of body in water = W₁

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

Upthrust = loss in weight when immersed in water = (W - W₁) gf    …[Eq 1]

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

Volume of water displaced = Volume of the body = V

Density of water = 1 g cm^-3

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

But weight of water displaced is equal to upthrust

∴ From eqns 1 & 2,

V = (W - W₁) cm³

∴ Volume of the body = V = (W - W₁) cm³

(ii) Upthrust = loss in weight when immersed in water = (W - W₁) gf

(iii) Relative density of the material of the body

= $\dfrac{\text {Weight of solid in air}}{\text {Weight in air - Weight in water}}$

= $\dfrac{W$1}{W1 - W_2}