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

Explanation

Consider the above given figure, here two vessels having same base area are shown. Let the volume of vessel (a) is 2V and that of vessel (6) is V. The water is filled upto height h in both the vessels, and assume that the density of water is p. As height of water column is same in two vessels of different shapes. Therefore, there will be same pressure exerted by the water on the base of each vessel that is `P_("atm")+hpg`. and hence the force on the bases of the vessels is also same. As water also exerts normal force on the walls of each vessel. As the walls are not perpendicular to the base of vessel so there must be some non-zero vertical component of the force exerted by water on the walls. This component is more in vessel (a) than in vessel (6). Hence, the vessels filled with the water even to same vertical height will show different readings on a weighing scale.