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 radius of r < r0 and a mass of m = m0.
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.

Explanation / Answer

1) new sphere is denser: If it still floats, it must displace the same amount of water (s);

if it sinks, it displaces less water (F): so "F or s"

.

2) as m < mo , level will fall

3) higher density means it can sink so, water level rises

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