Four cuboids with identical length, breadth and height are immersed in water.

 Question 46

Four cuboids with identical length, breadth and height are immersed in water. The cuboids are held at the same depth and in identical orientations by vertical rods, as shown.

Water has density ρ.

Cuboid W is made of material of density 4ρ.

Cuboid X is made of material of density 2ρ.

Cuboid Y is made of material of density ρ.

Cuboid Z is made of material of density 0.5ρ.

 

Which statement is correct?

A The upthrust of the water on each of the cuboids is the same.

B The upthrust of the water on W is twice the upthrust of the water on X.

C The upthrust of the water on X is twice the upthrust of the water on W.

D The upthrust of the water on Y is zero.

 

 

 

Reference: Past Exam Paper – June 2015 Paper 13 Q14

 

 

 

Solution:

Answer: A.

From Archimedes’ principle, the upthrust on an object under water is the weight of water displaced by the object. So, the upthrust is the same on each of the cuboids.

Alternatively, we know that upthrust is due to the pressure difference at the top and bottom surface of the object.

ΔP = Δhρg                   where ρ is the density of the liquid

Since the cuboids are have identical heights, the pressure difference and hence, the upthrust is are the same.

Note that in the above equation, ρ is the density of the liquid and NOT the density of the cuboids.