Two vessels `A` and `B` have same base area. Equal volumes of a liquid are poured in the two vessel to different heights `h_(A)` and `h_(B) (h_(B)gth_(A))`. In which vessel, the force on the base of vessel will be more?

Explanation

To determine in which vessel the force on the base will be more, we can follow these steps:

### Step 1: Understand the problem
We have two vessels, A and B, with the same base area. Equal volumes of liquid are poured into each vessel, but the heights of the liquid differ, with \( h_B > h_A \).

### Step 2: Define the forces acting on the base
The force exerted on the base of each vessel can be calculated using the formula:
\[ F = P \times A \]
where \( F \) is the force, \( P \) is the pressure at the base, and \( A \) is the area of the base.

### Step 3: Calculate the pressure at the base of each vessel
The pressure at the base of a liquid column is given by:
\[ P = \rho g h \]
where \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the height of the liquid column.

For vessel A:
\[ P_A = \rho g h_A \]

For vessel B:
\[ P_B = \rho g h_B \]

### Step 4: Calculate the forces on the base of each vessel
Using the pressure calculated in the previous step, we can find the forces on the base of each vessel.

For vessel A:
\[ F_A = P_A \times A = (\rho g h_A) \times A \]

For vessel B:
\[ F_B = P_B \times A = (\rho g h_B) \times A \]

### Step 5: Compare the forces
Since the base areas \( A \) are the same for both vessels, we can compare the forces by comparing the heights:
\[ F_A = \rho g h_A A \]
\[ F_B = \rho g h_B A \]

Given that \( h_B > h_A \), it follows that:
\[ F_B > F_A \]

### Conclusion
The force on the base of vessel B is greater than the force on the base of vessel A.