Effects on water level when a sphere is replaced by a new solid sphere

[marisalyn21]

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


I thought it was:
1) F
2) F or U or R
3) R
4) F
5) R
6) F

Could someone please help me figure out where I went wrong?

 

[barryj]

I would suggest that you first draw a diagram of the situation. Start with a ball in a tube of water and calculate the height of the water based on p0, r0, and m0. Then look at the equation and see what the effects would be. Use Archimedes principal of course.

 

[marisalyn21]

I have done that, but I'm still having trouble

 

[darkxponent]

It is density which effects the position of sphere,whether it floats,sinks and the volume that floats. so find the density for each part.

 

[barryj]

This problem is a little harder than it looks because it is more than finding the buoyancy force, you have to relate the displaced volume to the heighth of the liquid in the vessel. You can use simple logic to answer some of the questions but on others you will probably have to do a good analysis.

 

[barryj]

Here is the issue as I see it. I you reduce the radius, keeping everything else the same then the level will go down. If you increase the density, the level will go up. If you do both at the same time what happens? Hmmmm..

 

[barryj]

Here is another thought. The buoyancy force is equal to the weight of the water displaced. So, the heavier the sphere, the greater the required buoyancy force and hence the weight of the water displaced and the more water displaced. In summary, the heavier the sphere the more water displaced so the level will rise. So, the question becomes what factors effect the weight of he sphere.