A small solid sphere of mass M0, of radius R0, and of uniform density 0 is place
ID: 1442583 • 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.
The new sphere has radius R < R0 and mass M = M0
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 radius R = R0 and density > 0
The new sphere has density = 0 and mass M > M0
Explanation / Answer
Since solid sphere (mass is through out the volume ) is floating that means the density of sphere is less than water . so the sphere will keep floating untill its density got increased and it becomes larger than that of water
so in condition 3, 4 , and 6 the sphere will keep floating
in condition 1 , 2 , and 5 it is not mentioned that to which value the density has been incresed , so the sphere in these conditions may float or may sink
the water level depends on two thing
1. whether the sphere is floating or sinking (if it sinks than water level will decrease, )
2. if sphere is still floating than water level depends on the mass of floating sphere (if mass got increased than to balance that mass more water volume is needed, thus water level will increase
so now solving each scenario
case 1
density has been increased so
if sphere floats than level will remain unchanged
if sphere sinks than level will decrease
case 2
if net effect increases mass and still sphere floats than water will rise
if net mass remains same and sphere floats than water level remain same
if net mass decreases and sphere floats tahn water level will fall
if sphere sinks than water level will fall
case 3
the level of water will remain unchanged (since mass is same )
case 4.
the water level will fall (mass is decreased )
case 5
if spehere floats than level will increase (since mass is increased )
if it sinks than water level will decrease
case 6
sphere will float and water level will rise
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