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

Use Archimedes's Principle.

answers for the following are either (r) (f) (s) (r or s) (f or s) (r or f or s)

1. The new sphere has a mass of m < m0 and a radius of r > r0.
2. The new sphere has a radius of r < r0 and a density of > 0.
3. The new sphere has a density of < 0 and a mass of m > m0.

Explanation / Answer

floating condition is

upward force is buoyany force = downward force wweight

rho*g*V = m*g

rho*g*(4/3)*pi*r^3 = m*g

1) for m< mo and r > ro

so dispalcing more volume of water so answer is water level rises - r

2) if r < ro and rho > rho_0,water level does not depend on the density of sphere

water level fall so the answer is f

3) since weight increases it tries to sink so water level rises

so the answer is r

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