Question

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 2.20 × 10³ kg/m³. What fraction of the specimen’s apparent volume is solid?

Answer 1

Density of air is approximately 1.29 kg/m^3.
Density of rock = 2.2 * 10^3 kg/m^3
Denisty of water = 1.0 * 10^3 kg/m^3


Let V be total volume of the rock.
Mass of rock in air = Density * Volume = 2.20 * 10^3 * V,
Weight of rock in air = m*g = 2.20 * 10^3 * 9.8 V = 21560 V

Weight of rock in water = 21560 V / 2 = 10780 V

Weight of rock in water = Weight of rock in air - Buoyant Force
10780 V = 21560 V - Buoyant Force
Buoyant Force = 10780

Since the buoyant force is one half of the weight of rock in air.
So, one half the rock’s volume is solid and one half the rock’s volume is air