Answer:
3.842 g/cm³
Step-by-step 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.