The pressure at the bottom of a tank of liquid is not proprtional to

Options

A. Acceleration due to gravity
B. Density of the liquid
C. Height of the liquid
D. Area of the liquid surface

Answer

To solve the question regarding the pressure at the bottom of a tank of liquid and to determine which quantity it is not proportional to, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Pressure**:
Pressure at a point in a fluid at rest is defined as the force exerted per unit area. The formula for pressure (P) is given by:
\[ P = \frac{F}{A} \]
where \( F \) is the force and \( A \) is the area.

2. **Identify the Force Acting on the Liquid**:
The force exerted at the bottom of the tank is due to the weight of the liquid above it. The weight (W) of the liquid can be expressed as:
\[ W = m \cdot g \]
where \( m \) is the mass of the liquid and \( g \) is the acceleration due to gravity.

3. **Express Mass in Terms of Density and Volume**:
The mass of the liquid can be expressed in terms of its density (\( \rho \)) and volume (V):
\[ m = \rho \cdot V \]
The volume of the liquid in the tank can be calculated as:
\[ V = A \cdot h \]
where \( A \) is the cross-sectional area of the tank and \( h \) is the height of the liquid column.

4. **Combine the Equations**:
Substituting the expression for volume into the weight equation gives:
\[ W = \rho \cdot (A \cdot h) \cdot g \]

5. **Calculate Pressure at the Bottom of the Tank**:
Now substituting the expression for weight into the pressure formula:
\[ P = \frac{W}{A} = \frac{\rho \cdot (A \cdot h) \cdot g}{A} \]
Simplifying this, we get:
\[ P = \rho \cdot h \cdot g \]

6. **Analyze the Proportionality**:
From the final expression \( P = \rho \cdot h \cdot g \), we can see that pressure is directly proportional to:
- Density (\( \rho \))
- Height (\( h \))
- Acceleration due to gravity (\( g \))

However, pressure is **not proportional** to the area (\( A \)) of the tank since the area cancels out in the calculation.

### Conclusion:
The pressure at the bottom of a tank of liquid is not proportional to the **area** of the liquid.