Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill up to a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases? If so, why do the vessels filled with water to that same height give different readings on a weighing scale?

Given,

Two vessels are having same base area.

Two vessels are filled with water.

We have,

Pressure, P = ρgh

Where,

ρ = density

g = acceleration due to gravity

h = height of the column

Thus, for given two vessels pressure only depends on height of the water column only.

Force at the base,

Hence, Force exerted on the base of two vessels is same.

Weight = mg

Where,

m = mass

g = acceleration due to gravity

Different volumes of two vessels have different mass. So, on weighing scale they show different readings.