Question

Refer to the previous problem. Suppose, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament. Calculate the volume of the cavities left that will allow the weights given in that problem.

Answer 1

Let the volume of cavity be v.

∴ Total volume of the Ornament(y) = Volume of gold + volume of cavity

∴ Total volume (y)=  36/19.3 + v

Using, Principle of Flotation,

The volume of the water displaced is also y cm³

The mass of the water displaced =y × 1  = y grams.

The weight of the water displaced = yg

yg = 2 g

∴ y = 2

∴  36/19.3 + v = 2

∴ v = 2 - 1.86

∴ v = 0.13 cm³.

Hope it helps.