A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of 0

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 density of > 0 and a radius of r = r0.

2.The new sphere has a radius of r < r0 and a mass of m = m0.

3.The new sphere has a radius of r = r0 and a mass of m < m0.

Select r/f/s/r or s /f or s for the three questions.

Explanation / Answer

1. since new sphere has same radius, but higher density, therefore more massive, it will displace more water, hence water level rises Ans: r

2. Sine new sphere has smaller radius, but same mass, therefore, it has to displace same volume of water to float as the old one. Ans: s

3. Since, new sphere has smaller mass, therefore to float , it will displace less water, hence water level falls. Ans: f

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