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Any physicist in the house?

X

xEDIT409

Banned
A small solid sphere of mass M0, of radius R0, and of uniform density r0 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.

R=Radius
R0= Initial Radiou
r=density
r0=inititial density
M=mass
M=initial Mass

1. The new sphere has radius R = R0 and mass M > M0
2. The new sphere has radius R > R0 and density r < r0
3. The new sphere has mass M = M0 and radius R > R0
4. The new sphere has mass M > M0 and density r = r0
5. The new sphere has density r = r0 and radius R < R0
6. The new sphere has density r > r0 and mass M = M0

I know:
1. R-Rises
2. RFU- Rises, Falls or Unchagned
3.U-Unchanged
and
5. Unchanged

but for the life of me, I can't figure 4 and 6 out.
 
Originally posted by: xEDIT409
1. The new sphere has radius R = R0 and mass M > M0
2. The new sphere has radius R > R0 and density r < r0
3. The new sphere has mass M = M0 and radius R > R0
4. The new sphere has mass M > M0 and density r = r0
5. The new sphere has density r = r0 and radius R < R0
6. The new sphere has density r > r0 and mass M = M0

I know:
1. R-Rises
2. RFU- Rises, Falls or Unchagned
3.U-Unchanged
and
5. Unchanged

but for the life of me, I can't figure 4 and 6 out.
Click to expand...

for 4, obviously the radius has to increase, and the mass increases too, so Rises.
For 6, the radius decreases, but the level will be Unchanged since it has to displace the same mass of water to keep floating. It will just float a little lower.

Why did you use "r" for density?

/edit: Oh, and your answer for 5 is wrong. If the radius decreases, but the density remains the same, it will displace less water and the level will Fall.
 
Originally posted by: xEDIT409
A small solid sphere of mass M0, of radius R0, and of uniform density r0 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.

R=Radius
R0= Initial Radiou
r=density
r0=inititial density
M=mass
M=initial Mass

1. The new sphere has radius R = R0 and mass M > M0
2. The new sphere has radius R > R0 and density r < r0
3. The new sphere has mass M = M0 and radius R > R0
4. The new sphere has mass M > M0 and density r = r0
5. The new sphere has density r = r0 and radius R < R0
6. The new sphere has density r > r0 and mass M = M0

I know:
1. R-Rises
2. RFU- Rises, Falls or Unchagned
3.U-Unchanged
and
5. Unchanged

but for the life of me, I can't figure 4 and 6 out.
Click to expand...

4. More mass, same density. Density = mass/volume. If density is the same, and mass increases, volume increases. More sphere displaced = water level rises. R - Rises.

6. Density greater, mass remains constant. Density = mass/volume. If the density is greater and mass remains the same, volume must decrease. Opposite of 4, F - Falls.

Edit: My 6 is wrong. Jagec's is right. I forgot the ball floated instead of was totally submerged.
 
If anyone is curious, I found the right answers:

R: The new sphere has radius R = R0 and mass M > M0
R or F or U: The new sphere has radius R > R0 and density r < r0
U: The new sphere has mass M = M0 and radius R > R0
R: The new sphere has mass M > M0 and density r = r0
F: The new sphere has density r = r0 and radius R < R0
F or U: The new sphere has density r > r0 and mass M = M0

THANKS TO EVERYONE WHO HELPED. 🙂
 
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