A solid weighs 277.5 g in air and 212.5 g when totally immersed in the liquid of density 0.9 g / cc. Calculate the density of the solid.

3.842 g/cm³

Explanation:

Three forces are acting on the solid: weight, normal force (apparent weight), and buoyancy.

∑F = ma

N - m g + ρf V g = 0

N - ρs V g + ρf V g = 0

ρs is the density of the solid and ρf is the density of the fluid it is submerged in.

Writing normal force in terms of apparent mass, N = mₐ g:

mₐ g - ρs V g + ρf V g = 0

mₐ - ρs V + ρf V = 0

mₐ = ρs V - ρf V

mₐ = V (ρs - ρf)

V = mₐ / (ρs - ρf)

Volume is constant, so:

mₐ / (ρs - ρf) = mₐ / (ρs - ρf)

277.5 / (ρ - 0.0) = 212.5 / (ρ - 0.9)

Cross multiply and solve:

212.5ρ = 277.5 (ρ - 0.9)

212.5ρ = 277.5ρ - 249.75

249.75 = 65ρ

ρ = 3.842

The density of the solid is 3.842 g/cm³.