Question

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.
Read it to me
R F U R or U F or U R or F or U  The new sphere has density ρ = ρ₀ and radius R < R₀
R F U R or U F or U R or F or U  The new sphere has density ρ > ρ₀ and mass M = M₀
R F U R or U F or U R or F or U  The new sphere has radius R > R₀ and density ρ < ρ₀
R F U R or U F or U R or F or U  The new sphere has mass M > M₀ and density ρ = ρ₀
R F U R or U F or U R or F or U  The new sphere has radius R = R₀ and mass M > M₀
R F U R or U F or U R or F or U  The new sphere has mass M = M₀ and density ρ < ρ₀

Think Archimedes Principle. How does the volume displaced by a floating object differ from the volume displaced by an object that sinks?

Answer 1

Let r= radius, m = mass, d= density