Question

Mathematical proof of upthrust is based on

• A. Definition of pressure
• B. Weight of object
• C. Pressure exerted by a column of fluid
• D. Viscosity

Answer 1

The correct option is C Pressure exerted by a column of fluid

Mathematical proof:

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 = $h\rho gA$

Force on the lower face of the cylinder = $[h+L]\rho gA$

Difference in force = $LA\rho g$

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.