Question

Water Level 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.

1.The new sphere has mass M = M0 and radius R < R0

2.The new sphere has mass M = M0 and density ? < ?0

3.The new sphere has radius R > R0 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 radius R < R0 and density ? > ?0

Think Archimedes Principle. How does the volume displaced by a floating object differ from the volume displaced by an object that sinks? Please include explanations!

Answer 1

According to Archimedes Principle, for a floating body in static equilibrium and in the absence of any other external force, the buoyant force must balance the weight of the body. (i.e weight of the body = weight of the fluid dispaced)

1. mass same (No change in the level);

2. mass same (No change in the level);

3. mass incresed as density and volume increasing (level increased)

4. mass increased (level increased)

5. density same but radius decreased means overall mass decreased (level falls)

6.radius decreased and density increased, we cannot say mass is decreasing or increasing (result will unknown)