Question

Show that upthrust is equal to the weight of liquid displaced by deducing an equation.

Answer 1

Explanation:

Consider a cylinder of cross section area A and height L completely submerged in water. Let depth of upper surface be h.

Using, pressure exerted by fluid column:

Force on the upper face of the cylinder = hρgA

Force on the lower face of the cylinder = [h+L]ρgA

Difference in force = LAρg

But LA is the volume of liquid displaced by the cylinder, and LrgA is the weight of the liquid displaced by the cylinder.

Therefore there is a net upward force on the cylinder equal to the weight of the fluid displaced by it.

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