A small solid sphere of mass M 0 , of radius R 0 , and of uniform density ? 0 is
ID: 1262454 • Letter: A
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 mass M = M0 and radius R < R0
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 mass M = M0 and density ? < ?0
R F U R or U F or U R or F or U The new sphere has density ? = ?0 and radius R > R0
R F U R or U F or U R or F or U The new sphere has density ? > ?0 and radius R < R0
R F U R or U F or U R or F or U The new sphere has mass M < M0 and density ? = ?0
Explanation / Answer
when that sphere is replaced by a new solid sphere of uniform density.
case- 1----------------------The new sphere has mass M = M0 and radius R < R0
Density, D= M/V
V= 4/3* pie * R3
V<V0
The new sphere has density D which is greater than D0, the old sphere; D> D0
Hence it sinks and water level L rises
case- 2---------------------The new sphere has density D> D0 and radius R =R0
The new sphere has density D which is greater than D0 the old sphere; D> D0
Hence it sinks and water level L rises
case-3---------------------The new sphere has mass M = M0 and density D< D0
The new sphere has density D which is less than D0 the old sphere;
Hence it floats and water level L unchanged
case-4---------------------The new sphere has radius R >R0 and density D=D0
The new sphere has density D equal to D0 the old sphere but radius greater,
Hence it floats and water level L unchanged
case-5---------------------The new sphere has radius R <R0 and density D>D0
The new sphere has density D greater than D0 the old sphere but radius less
Hence it sinks and water level L rises
case-6---------------------The new sphere has mass M < M0 and density D=D0
The new sphere has density D equal to D0 the old sphere but mass less
Hence it floats and water level L unchanged
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