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.

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

Answer 1

stays same

Since the mass has not changed. So the volume of water displaced remains same and water level stays same

Rise

Since mass has increased. So the volume of water displaced will increase and that in turn increases the water level.

Rise

For the same size of the sphere, the density has increased. This increases the mass of sphere since mass is the product of density and volume. As mass of sphere increase, it displace more volume of water. hence the water level rise.