A small solid sphere of mass M0, of radius R0, and of uniform density p0 is plac

Question

A small solid sphere of mass M0, of radius R0, and of uniform density p0 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.   each question can be R, F, U,            R or U,           F or U, or          R or F or U    6 different options

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

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

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

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

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

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

Explanation / Answer

1) water level rises (R) as due to large density solid will be more submerged hence displacing more water equavelent to its weight

2) falls (F) as weight decreases because volume decreases and hence the water displaced

3) remains unchanged (U) as because water displaced will be same

4) remains unchanged (U) as the water displaced will be same

5) if mass of the new sphere is more than it will rise the height but if mass of the new sphere is less than height decreases also mass can be equal hence answer ( R or U or F)

6) since mass will be more hence the height increases ( R)

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