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.

Choices:

1) R

2) F

3) U

4) R or U

5) F or U

6) R or F or U

The new sphere has density > 0 and mass M = M0
The new sphere has mass M = M0 and radius R > R0
The new sphere has radius R < R0 and density > 0
The new sphere has mass M > M0 and density = 0
The new sphere has radius R = R0 and mass M > M0
The new sphere has density = 0 and mass M < M0

Explanation / Answer

Case 1 :                   The new sphere has density > 0 and mass M = M0

mass remains same , so Volume of liquid displaced remains same, hence water level is unchanged U

Case 2 : The new sphere has mass M = M0 and radius R > R0

mass remains same , so Volume of liquid displaced remains same, hence water level is unchanged U

case 3: The new sphere has radius R < R0 and density > 0

Volume is decreased and mass is increased , hence mass remains unchanged, so Volume of liquid displaced remains same, hence water level is unchanged U

case 4 : The new sphere has mass M > M0 and density = 0

mass has increased , so Volume of liquid displaced will increase, hence water level is unchanged Rises R

case 5 : The new sphere has radius R = R0 and mass M > M0

mass has increased , so Volume of liquid displaced will increase, hence water level   Rises R

case 6 :The new sphere has density = 0 and mass M < M0

mass has decreased , so Volume of liquid displaced will decrease, hence water level   Falls F

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