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.

The new sphere has density < 0 and mass M = M0

The new sphere has density < 0 and radius R > R0

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

The new sphere has mass M > M0 and density = 0

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

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

options are R, U, f, R OR U, f OR U, R OR f OR U

Explanation / Answer

1) lower density, greater radius; mass might go up, down, or stay same:
R or F or U
2) smaller mass: F
3) larger radius, same density, so larger mass: R
4) same mass: U
5) same mass: U
6) same radius, greater density, so greater mass: R

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