A small solid sphere of mass M0, of radius R0, and of uniform density 0 is place

Question

A small solid sphere of mass M0, of radius R0, and of uniform density 0 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.

In addition to R,F, or U answers can also be R and U, F and U, or R, F, and U. Therefore, there are six options for each.

1) The new sphere has radius R = R0 and mass M > M0
2) The new sphere has radius R > R0 and density < 0
3) The new sphere has density = 0 and radius R > R0
4) The new sphere has radius R < R0 and density = 0
5) The new sphere has radius R < R0 and mass M = M0
6) The new sphere has mass M = M0 and radius R > R0

Explanation / Answer

1) The new sphere has radius R = R0 and mass M > M0 = rises

2) The new sphere has radius R > R0 and density < 0 = rises , fall or unchanged

3) The new sphere has density = 0 and radius R > R0 = rises

4) The new sphere has radius R < R0 and density = 0 = falls

5) The new sphere has radius R < R0 and mass M = M0 = rises

6) The new sphere has mass M = M0 and radius R > R0 = rises or unchanged

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