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.

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

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

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 density < 0 and mass M = M0

Explanation / Answer

A floating object displaces an amount of water of the same mass, so following coclusions is inferred -

1) F Size decreased (As Radius Decreased) = mass decreased = level falls.
2) R Same radius, greater density, so greater mass = level rises.
3) U As Mass Remains Same , Therefore Unchanged.
4) R Greater radius, same density, so greater size = mass increased = level rises.
5) R or F or U Density increased but size decreased.therefore mass might remain same or increas or decrease depending upon the change in quantities..
6) U As Mass Remains Same , Therefore Unchanged.

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