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.

1. The new sphere has a radius of r = r0 and a mass of m < m0.
2. The new sphere has a radius of r = r0 and a density of ? < ?0.
3. The new sphere has a mass of m = m0 and a radius of r < r0.

Explanation / Answer

Case (1) -

Radius is same, means volume of the sphere V is constant. But m< m0, means mass is less.

So, density of the sphere, (m/V) shall be less.

So, volume of displaced water will be less.

Therefore, our answer is 'water level falls,(f)'.

(2) Same condition as mentioned above.

So, correct answer is 'f'.

(3) m = m0, means mass is constant.

r < r0, means volume is less.

So, density is bigger.

So, water level rises.

Hence, 'r' is the correct answer.

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