The weight of a solid is 80g in air and 50g in a liquid of relative density 1.5. Calculate the relative density of the solid.

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Solution

The correct option is D
4

Loss of weight of solid in liquid = (80-50)g = 30g

Weight of equal volume of liquid by Archimedes principle = 30g

If the liquid displaced has a volume of $V c m^{3}$ , then it's weight $= V \times 1.5 = 30 g$

Therefore, $V = 20 c m^{3}$

Since solid is completely immersed in liquid, so volume of solid = V

The volume of water that will be displaced by same solid $= 20 c m^{3}$

Therefore weight of this displaced water = 20g

So we have specific gravity of solid = weight of solid in air/weight of water displaced $= \frac{80 g}{20 g} = 4$

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