A small solid sphere of mass M 0 , of radius R 0 , and of uniform density 0 is p

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.
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R F U R or U F or U R or F or U  The new sphere has radius R > R0 and mass M = M0
R F U R or U F or U R or F or U  The new sphere has mass M = M0 and density > 0
R F U R or U F or U R or F or U  The new sphere has radius R = R0 and density > 0
R F U R or U F or U R or F or U  The new sphere has radius R < R0 and density = 0
R F U R or U F or U R or F or U  The new sphere has radius R < R0 and density > 0
R F U R or U F or U R or F or U  The new sphere has radius R > R0 and density = 0

Explanation / Answer

Disagree with 1st answer on 5th case:
The new sphere has radius R = R0 and mass M < M0:
falls
The new sphere has mass M < M0 and density r = r0:
falls
The new sphere has radius R > R0 and density r < r0:
depends on mass; ball still floats & displaces its mass; greater = rises; less = falls; same = unchanged
The new sphere has density r = r0 and mass M > M0:
rises
The new sphere has density r > r0 and mass M = M0:
depends on density; if > water density ball sinks & only displaces volume so level falls; otherwise unchanged
The new sphere has radius R > R0 and mass M = M0:
unchanged

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