Question

A cylinder is floating in a beaker containing two liquids. The heights h₁​ and h₂​ of the cylinder are submerged in the liquids of densities rho₁​ and rho₂​. What will be the submerged length of the cylinder in fluid 2 if we increase the height of fluid 1 above fluid 2?

Options:
a. The submerged length remains unchanged.
b. The submerged length increases.
c. The submerged length decreases.
d. The change cannot be determined without additional information.

Answer 1

The result of the increase in the height of fluid 1 would be c. The submerged length decreases.

What happens to the fluid ?

The pressure at any point in a fluid at rest is given by Pascal's law and is equal in all directions. When the cylinder is in equilibrium, the pressure at its top and bottom must be equal.

As fluid 1 is raised above fluid 2, the pressure at the bottom of the cylinder in fluid 2 will increase due to the increased height of fluid 1 above it. To maintain equilibrium, the cylinder will adjust by sinking further into fluid 2, decreasing its submerged length in fluid 2.