Question

Describe an experiment, using AA body weighs W1 gf in air and when immersed in a liquid, it weighs W2 gf, while it weighs W3 gf on immersing it in water. Find: (i) volume of the body (ii) upthrust due to liquid (iii) relative density of the solid and (iv) relative density of the liquid.rchimedes’ principle, to find the relative density of a liquid.

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Answer

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

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