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 'r or f or s' are possible answers in some of the cases.

[ r, f, s, r or s, f or s, r or f, or s ] The new sphere has a density of ρ > ρ₀ and a radius of r < r₀.
[ r, f, s, r or s, f or s, r or f, or s ] The new sphere has a density of ρ < ρ₀ and a mass of m > m₀.
[ r, f, s, r or s, f or s, r or f, or s ] The new sphere has a mass of m < m₀ and a radius of r > r₀.

Answer 1

when a body is either partially or fully submerged in a fluid it experience a net vertical force and this force known as buoyancy force. According to Archimedes buoyancy force is equal to weight of fluid displaced .