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

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

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 radius of r < r0.

Explanation / Answer

1. It's water level will fall (f)

Since it have low mass and large density due to which it have low volume and it will displace low volume

2. It's water level may rise and may fall or remain same (r or f or s)

Since we didn't have any idea about its mass we can't say anything.

3. Water level will rise (r)

Since it have larger mass it will displace larger amount of water whoes weight is eual to weight of new sphere

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