Question

Rocky enjoys snuba diving, which is combination of scuba diving and snorkeling. One day he notices two large metallic slabs that have sunk to the bottom of a nearby lake. He brings them to the shore and determines one to be aluminum (density 2.7 g/cm3) and the other to be lead (density 11.3 g/cm3). Both slabs weigh 10 kg. Which slab is associated with the larger buoyancy force?

Answer 1

From Pascal's principles we know that when a body is immersed in a liquid there is a balance between the weight and the buoyancy force exerted by the liquid. This pushing force is equal to the weight of the liquid displaced by it. The mathematical description of this force is given as,

`F_B = V\rho g`

Here,

V = Volume of the Object immersed

`\rho` = Density of liquid

g = Gravity

The values of our materials are,

Density of Al = 2.7 gm/cc

Density of Lead = 11.3 gm/cc

Both slabs has the same mass (10 kg)

A direct conclusion we have is that Al is less dense than Lead, therefore Al slab will have a larger volume than lead.

Hence, Al slab will be associated with the larger buoyant force.