A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of 0

Question

A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of 0 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.

The new sphere has a mass of m = m0 and a radius of r < r0.

The new sphere has a density of < 0 and a radius of r = r0.

The new sphere has a mass of m > m0 and a radius of r = r0.

Use Archimedes's Principle.

Explanation / Answer

for m = mo and r < ro ,then density rho > rho_o,then sphere sinks ,so water level rises (r)

for density rho < rho_o and r = ro,then sphere floats ,so water level is same

for m > mo and r = ro ,the sphere sinks,so water level rises (r)

so the answers are

r s r

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