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 × density of water × g
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
∴ 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
W_1\over W_1 - W_2