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.

Select r, f or s for the following statements:

The new sphere has a density of < 0 and a radius of r = r0.
The new sphere has a radius of r < r0 and a mass of m = m0.
The new sphere has a radius of r = r0 and a mass of m > m0.

Explanation / Answer

(i)

If the displaced volume of the water increases, the water level increases. The displaced water does not depend on the mass of the object.

In the first case the new density of the sphere is less than the initial sphere's density. Due to the low density than the previous sphere, it will dip low and it will displace the small amount of water than the previous sphere.

Therefore, the water level falls.

Answer is '' F''

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(ii)

In this case new sphere's radius is less than the initial radius of the sphere. So it will occupy the small volume of th water.

Therefore, the water level falls..

Answer is '' f''

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(iii)

In the third case the new the radius of the sphere is same as in the initial radius of the sphere. There is not change in the volume of the displaced water.

therefore, the water level does not change.

Answer is " S''

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