Arock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) what mass of water is displaced? (b) what is the volume of the rock? (c) what is its average density?

(a) 198 g

When the rock is submerged into the water, there are two forces acting on the rock:

- its weight, equal to (m=mass, g=acceleration of gravity), downward

- the buoyant force, equal to (=mass of water displaced), upward

So the resultant force, which is the apparent weight of the rock (W'), is

which can be rewritten as

where m' is the apparent mass of the rock. Using:

m = 540 g

m' = 342 g

we find the mass of water displaced

(b)

If the rock is completely submerged, the volume of the rock corresponds to the volume of water  displaced.

The volume of water displaced is given by

where

is the mass of the water displaced

is the density of the water

Substituting,

And so this is also the volume of the rock.

(c)

The average density of the rock is given by

where

m = 540 g = 0.540 kg is the mass of the rock

is its volume

Substituting into the equation, we find

at right angles to each other