Three blocks, labeled A, B, and C, are floating in water as shown in the drawing. Blocks A and B have the same mass and volume. Block C has the same volume, but is submerged to a greater depth than the other two blocks. Which one of the following statements concerning this situation is false?
A)The density of block A is less than that of block C.
B)The buoyant force acting on block A is equal to that acting on block B.
C)The volume of water displaced by block C is greater than that displaced by block B.
D)The buoyant force acting on block C is greater than that acting on block B.
E)The volume of water displaced by block A is greater than that displaced by block B.

Question

Three blocks, labeled A, B, and C, are floating in water as shown in the drawing. Blocks A and B have the same mass and volume. Block C has the same volume, but is submerged to a greater depth than the other two blocks. Which one of the following statements concerning this situation is false? 
A)The density of block A is less than that of block C. 
B)The buoyant force acting on block A is equal to that acting on block B. 
C)The volume of water displaced by block C is greater than that displaced by block B. 
D)The buoyant force acting on block C is greater than that acting on block B. 
E)The volume of water displaced by block A is greater than that displaced by block B.

Quizplus · Accepted Answer

According to Archimedes' principle, the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by that object. Since blocks A and B have the same mass and volume, their densities (mass/volume) must be equal as well.

Block C, on the other hand, is submerged to a greater depth, which means it displaces more water and experiences a greater buoyant force. Therefore, statement D is true.

Statement A is also true since block C is submerged to a greater depth than block A, which means it must displace more water and have a greater density.

Statement B is true since blocks A and B have the same volume and are submerged to the same depth, so they experience the same buoyant force.

Statement C is true since block C is submerged to a greater depth, which means it displaces more water than block B.

The false statement is E because blocks A and B have the same volume, so they displace the same amount of water. Therefore, the volume of water displaced by block A is not greater than that displaced by block B.

Three Blocks, Labeled A, B, and C, Are Floating in Water