Question

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.

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Answer

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

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