A solid, homogeneous sphere with a mass of m 0 , a radius of r 0 and a density o

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

Explanation / Answer

1) According to Archemedes Principle, the water level will rise for the first case.

2) Here density of the new sphere is less, so mass is less. radius of both sphere is same so there is no change in the volume. i.e. mass of new sphere is less. In this case water level falls.

3) mass of new sphere is same but density is more i.e. volume of new sphere is less so radius of new sphere is less. in this case, water level stays same because mass is same for both sphere. Here we applied the concept of Archemedes Principle.

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