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.

1) The new sphere has a mass of m = m0 and a radius of r > r0. (r, f, or s)
2) The new sphere has a density of = 0 and a mass of m > m0. (r, f, or s)
3) The new sphere has a density of = 0 and a radius of r < r0. (r, f, or s)

Explanation / Answer

Solution:

1) r

mass same

r increased => volume of sphere increases => water level rises!

2) r

density same and mass increased

as we know;

mass = density * volume

=> volume must have increased to increase the mass

hence

water level rises!

3) f

same density

but radius decreased(r < r0)

=> volume of the sphere decreased

=> fall in water level!

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