A small solid sphere of mass M0, of radius R0, and of unifor

[Spartan73]

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.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/sound/waterLevelCpt.mp3
1.The new sphere has density ρ = ρ0 and radius R > R0
2.The new sphere has radius R < R0 and density ρ = ρ0
3.The new sphere has radius R = R0 and density ρ < ρ0
4.The new sphere has density ρ < ρ0 and mass M = M0
5.The new sphere has radius R < R0 and density ρ > ρ0
6.The new sphere has density ρ > ρ0 and mass M = M0

Homework Equations

The Attempt at a Solution

1 R
2.F
3. F
4. U
5. R,F,U
6. U

 

[superkraken]

for 3.i think it will rise because the force by water is ρ(of water) x volume x g(acc. due to gravity).if ρ is less than ρ(water)

 

[berkeman]

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.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/sound/waterLevelCpt.mp3
1.The new sphere has density ρ = ρ0 and radius R > R0
2.The new sphere has radius R < R0 and density ρ = ρ0
3.The new sphere has radius R = R0 and density ρ < ρ0
4.The new sphere has density ρ < ρ0 and mass M = M0
5.The new sphere has radius R < R0 and density ρ > ρ0
6.The new sphere has density ρ > ρ0 and mass M = M0

Homework Equations

The Attempt at a Solution

1 R
2.F
3. F
4. U
5. R,F,U
6. U

Please show your work/reasoning behind your answers...

 

[haruspex]

Be careful with 6. What are all the possible consequences of increased density?