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

r f s r or s f or s r or f or s  The new sphere has a mass of m > m0 and a density of ? < ?0.
  r f s r or s f or s r or f or s The new sphere has a mass of m < m0 and a radius of r > r0.
  r f s r or s f or s r or f or s  The new sphere has a density of ? < ?0 and a radius of r > r0.

Explanation / Answer

1. Since mass of new sphere is more, it requires more Buoyant Force to balance its weight, therefore more level rise

Answer : r

2.

Since mass of new sphere is less, it requires less Buoyant Force to balance its weight, therefore level falls

Answer : f

3. Since Density is decreased, but at the same time radius is increased, it is not certain whether mass is increased or not, therefore Answer : r or f or s

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