Weight of the body in air = W1 gf
Weight of the body in liquid = W2 gf
Weight of the body in water = W3 gf
(i) Let V be the volume of the body.
Upthrust due to water = loss in weight when immersed in water = (W1 – W3) 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 = (W1 – W3) cm3
∴ Volume of the body = V = (W1 – W3) cm3
(ii) Upthrust due to liquid = loss in weight when immersed in liquid = (W1 – W2) 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