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

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.

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

Choices are R-Rises, F-Falls, U-Unchanged, R or U, F or U, R or F or U

Please Help! Thank you so much

Explanation / Answer

You appear to have left out part of the question immediately after '...a large bowl containing'. So the question doesn't make sense. I expect the answers depend on working out the density in the different cases. Floating/sinking can be decided upon by only considering density: - if the density of an object is less than water's density, the object will float. - if the density of an object is equal to water's density, the object will have neutral buoyancy (stay at any fixed submerged position). - if the density of an object is more than water's density, the object will sink.

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