Question

In a liquid medium, if the depth increases, the pressure at that place ________.

• A. decreases
• B. increases
• C. remains constant
• D. depends on the shape of the container
• E. is zero

Hint:

Pressure in a liquid = Atmospheric Pressure + $\rho gh$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
This question is about the pressure within a fluid (hydrostatic pressure). The pressure at a certain depth in a fluid is due to the weight of the fluid column above that point.
Step 2: Key Formula or Approach
The pressure \(P\) at a depth \(h\) below the surface of a liquid with a constant density \(\rho\) is given by the formula:
\[ P = P_0 + \rho g h \] where:
- \(P_0\) is the pressure at the surface (usually atmospheric pressure).
- \(\rho\) is the density of the liquid.
- \(g\) is the acceleration due to gravity.
- \(h\) is the depth.
The pressure due to the liquid column itself is called the gauge pressure, given by \(P_{gauge} = \rho g h\).
Step 3: Detailed Explanation
1. Analyze the pressure formula.
The formula \(P = P_0 + \rho g h\) shows the relationship between pressure \(P\) and depth \(h\).
The terms \(P_0\), \(\rho\), and \(g\) are generally considered constant for a given situation.
Therefore, the pressure \(P\) is a linear function of the depth \(h\).
2. Determine the effect of increasing depth.
As the depth \(h\) increases, the term \(\rho g h\) also increases (since \(\rho\) and \(g\) are positive).
This means that the total pressure \(P\) increases.
The pressure increases linearly with depth.
3. Evaluate the options.
- (A) decreases: Incorrect.
- (B) increases: Correct.
- (C) remains constant: Incorrect. Pressure is only constant at the same horizontal level.
- (D) depends on the shape of the container: Incorrect. This is a common misconception. The pressure at a given depth depends only on the depth and the fluid density, not the width or shape of the container (this is known as the hydrostatic paradox).
- (E) is zero: Incorrect.
Step 4: Final Answer
If the depth increases, the pressure at that place increases.