Question

You have a piece of metal of unknown origin and type. Provided you have the ability to measure the weight of the piece of metal both in air and in water (W_air, W_H2O), and know the density of air and water (density_air,density_water), determine the density and the specific gravity of the metal.

Hint: draw a free body diagram for each fluid, and use Archimedes’ principle.

Do not make any simplifying assumptions regarding density ratios -- until the end, when you should comment on the magnitude of each of the terms that may arise in your solution.

Answer 1

According to archimedes principle, the buoyant force experienced by a submerged object is equal to the weight of the liquid displaced by the object.

Experimentally, it turns out that weight of the liquid displaced is equal to the difference between the weight of the object measured in air and in water.

Therefore,

  

So,

Density of metal is

Where d is the density of water, and g is the acceleration dur to gravity.

Now, specific gravity is the ratio of density of substance to the density of water.

From the above equation , we can also find the specific gravity of the metal, that is