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

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.

The new sphere has a density of ? = ?0 and a mass of m < m0.
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 density of ? < ?0.

Explanation / Answer

According to Archimedes' principle the buoyant force is equal to the weight of the displaced fluid. (i.e weight of the object = wieght of liquid displased)

and we know, mass = volume x density;

a) mass decreased (level falls)

b) radius decreased but density constant i.e. mass decreased (level falls)

c) mass same (lavel remains same).

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