Question

A solid, homogeneous sphere with a mass of m₀, a radius of r₀ and a density of ρ₀ is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'f or s' are possible answers in some of the cases.

1. The new sphere has a radius of r > r₀ and a density of ρ = ρ₀.
2. The new sphere has a mass of m < m₀ and a density of ρ = ρ₀.
3. The new sphere has a mass of m = m₀ and a radius of r > r₀.

4. The new sphere has a density of ρ < ρ₀ and a radius of r = r₀.
5. The new sphere has a mass of m = m₀ and a radius of r < r₀.
6. The new sphere has a radius of r = r₀ and a mass of m < m₀.

7. The new sphere has a mass of m > m₀ and a density of ρ < ρ₀.
8. The new sphere has a density of ρ < ρ₀ and a radius of r > r₀.
9. The new sphere has a mass of m < m₀ and a radius of r > r₀.

Answer 1

Summary:According to Archimedes principle the weight of body immersed in fluid is equal to the weight of fluid displaced by body.