The three vessels shown in Fig. 8.33( A-C) have exactly the same base area. Equal volumes of a l

step 1 One question, we are given three vigils, three vessels. Let's draw these veggles. This is vessel

The three vessels shown in Fig. 8.33( A-C) have exactly the...

The three vessels shown in Fig. $8.33(\mathrm{~A}-\mathrm{C})$ have exactly the same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be (A) Maximum in vessel $\mathrm{A}$ (B) Maximum in vessel $\mathrm{B}$ (C) Maximum in vessel $\mathrm{C}$ (D) Equal in all the vessels

The three vessels shown in Fig. $8.33(\mathrm{~A}-\mathrm{C})$ have exactly the same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be
(A) Maximum in vessel $\mathrm{A}$
(B) Maximum in vessel $\mathrm{B}$
(C) Maximum in vessel $\mathrm{C}$
(D) Equal in all the vessels

Key Concepts

Weight of the Fluid

Regardless of the shape of the vessel, if the volume and density of the fluid are the same, then the total weight of the fluid remains constant. The force exerted by the fluid on the base is equal to its weight, making this concept essential for determining how the force is distributed in different container shapes.

Pressure Distribution in Containers

While the geometry of a container can affect the local pressure distribution across the base, when the base area is the same and the total volume (and thus the weight) of the fluid is identical, the integrated effect of the pressure over the entire base leads to the same net force. This shows that the overall force on the base is not dependent on the detailed shape of the liquid’s free surface.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It is calculated as the product of the fluid’s density, the gravitational acceleration, and the depth of the fluid. This concept is central in understanding how pressure varies with height in a fluid column.

Force Due to Fluid Pressure

The force on a surface submerged in a fluid is determined by the product of the pressure acting on it and the area of the surface. In scenarios where the base area is constant, any differences in the pressure distribution would change the force if only local pressure were considered; however, the overall force acting on the base is directly related to the weight of the fluid above it.

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