Scaling law for static buoyancy

[farahtc]

Homework Statement

Derive the scaling law for static buoyancy force of a solid sphere in a liquid with a density of γ.
Assume the sphere is made of a material with a density of γs (γs< γ).

Homework Equations

The Attempt at a Solution

I calculated the the buoyancy force of the sphere as

F=(pi/6)*d^3*γ*g, where F=buoyancy force, d=sphere diameter. NOw can anybody tell me what is scaling law?how to derive it?

 

[Michaud12]

Im doing this exact same problem in my MEMS class and i have the same issue