Homework Help: Buoyancy With Solid Sphere

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1. Nov 9, 2015

ScrubTier

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.
The new sphere has radius R > R0 and mass M = M0
The new sphere has radius R < R0 and density ρ = ρ0
The new sphere has mass M = M0 and density ρ > ρ0
The new sphere has mass M > M0 and density ρ = ρ0
The new sphere has radius R = R0 and mass M > M0
The new sphere has radius R < R0 and density ρ > ρ0

2. Relevant equations
B=mass/volume

3. The attempt at a solution
1. U
If it is not submerged then the displacement is equal to mass which doesn't change
2. F
This means less mass therefore less displacement
3. U
If it is not submerged then the displacement is equal to mass which doesn't change
4. R
More displacement
5. R
More displacement
6. R or F or U
It depends how it effects the mass

2. Nov 9, 2015

haruspex

Not bad, but in a couple of places you wrote "if it is not submerged". You need to decide whether it can be submerged and if so how that affects the answer.

3. Nov 9, 2015

ScrubTier

1. R or U
Floating: U mass doesn't change
Submerged: Radius increase means more displacement
2. F
To keep p constant both must fall
3. F or U
Floating: U mass doesn't change
Submerged: To get p to be larger with m constant then volume must decrease
4. R
If Mass increases but p stays constant then volume must also increase. Displacement increases in both situations
5. R or U
Floating: R Mass increases therefore more displacement
Submerged: U volume remains constant no change
6. R or F or U
Floating: Mass may or may not increase could be Rise or U
Submerged: Volume decreases therefore F

This is still wrong. I really can't tell why.

4. Nov 9, 2015

haruspex

You are told it is floating initially. What you have to consider is which of the proposed changes might result in the sphere sinking, and how that might affect the change in water level.

5. Nov 9, 2015

ScrubTier

In 1, 2,4 It would not submerge
so 1. Would be no change because not submerging and mass no change
2. Fall because p being the same, R getting smaller, than M must also get smaller
4. Rise because p is the same, M gets larger
?

6. Nov 9, 2015

haruspex

Right.
What about 3, 5 and 6?

7. Nov 10, 2015

ScrubTier

Well doesn't it depend on if it actual sinks? Like how much the density changes which I don't know?

8. Nov 10, 2015

haruspex

That's right. For the cases where the density increases, consider both possibilities. If this leads to different answers for R, F, U, list all those that may occur.
(For at least one of 3, 5, 6, not all of R, F, U are possible.)