Effects of New Solid Sphere on Water Level

[gummybeargirl]

Homework Statement

A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

1) The new sphere has mass M < M0 and density ρ = ρ0
2) The new sphere has density ρ = ρ0 and radius R > R0
3) The new sphere has mass M = M0 and radius R > R0
4) The new sphere has radius R = R0 and mass M < M0
5) The new sphere has mass M = M0 and density ρ > ρ0
6) The new sphere has density ρ < ρ0 and radius R > R0

2. The attempt at a solution
1) F (less mass means displaces less water)
2) R (larger radius displaces more water)
3) R or U (if the density is lower it would be unchanged, but it could rise)
4) F or U (it would displace more less water, unless the density increased)
5) R (it would sink increasing water level)
6) R or F or U (it could sink or float or not change it at all)

 

[Nathanael]

1) F (less mass means displaces less water)

Answer is correct, but I think your explanation is unsatisfactory.

3) R or U (if the density is lower it would be unchanged, but it could rise)

The density IS lower (same mass, more volume) but why could that mean it's unchanged?

4) F or U (it would displace more less water, unless the density increased)

The density is necessarily decreased (same volume, less mass)

5) R (it would sink increasing water level)

Would it sink? ρ0 is not the density of water

6) R or F or U (it could sink or float or not change it at all)

Yes, this is the only one with an uncertain answer (it depends on how much R/ρ are changed)