## Question

A metal nugget floats in between some water and mercury. The densities of the metal nugget, mercury and water are 7900 kg m^{-3}, 13600 kg m^{-3} and 1000 kg m^{-3} respectively.

What is the ratio of the volume of the nugget submerged in water to that of mercury?

A) 0.541

B) 0.826

C) 0.924

D) 1.21

## Answer

Since the nugget is suspended in the liquids, the weight of the nugget is equal to the upthrust.

The nugget displaces both water and mercury, hence, the upthrust is due to the both the weight of the water displaced and the weight of the mercury displaced.

The volume of the nugget is the sum of the volume of water displaced and the volume of mercury displaced.

The answer is B.