9702_s22_qp_13 Question 15

A block of wood of density ρ_W has sides of length a. The block is immersed in a liquid of density ρ_L. 

The top surface of the block is at a depth h below the surface of the liquid.  

The acceleration of free fall is g. 

What is the upthrust acting on the block from the liquid? 

A  ρ_La³g 

B  ρ_Wa³g 

C  ρ_Lhg 

D  ρ_Lag

ANSWER: A

The Physics behind the answer:

• Archimedes Principle quantifies upthrust as equal in magnitude to the weight of the fluid displaced by the object submerged in that liquid. This means that the upthrust is equal to the mass of displaced liquid multiplied by the acceleration due to gravity. 

upthrust = mg

• The mass of displaced liquid is equal to the density of liquid multiplied by volume of displaced liquid.

m = ρV

• The volume of the displaced liquid, then, is equal to the volume of the object completely submerged in it. In the case of the problem, it is the volume of cube.

V = a³

• Combing the equations above, it can be shown that

upthrust = ρa³g