How do I solve this problem?

Question

Cork has a density of 0.24 g/cm³. Assuming water has a density of 1.00 g/cm³, what percentage of a cork stopper will be submerged under water if it is floating on the surface? What percentage would be above the surface?

Answer 1

By Archimedes Law: ρVg = ρ₁V₁g, where V₁ is volume under water. V₁ = ρV/ρ₁·100% = 0.24V/1.00·100% =

24% of V and above water level part = 100% - 24% = 76% of V

Answer 2

Assume the volume of a cork stopper is V cm³

Then the mass is 0.24V g, or 0.00024V kg

Weight = 0.00024 x 9.81 V N

Buoyant force must be the same.

This is weight of water displaced.

So if X is volume of water displaced in cm³, weight of water displaced in kg is 0.001 X x 9.81

So 0.001 X x 9.81 = 0.00024 x 9.81 V

So X = 0.24 V

So 24% of the cork stopper will be submerged

76% above the surface