The Question is from NEET guide , and it was created by the author SUBHANI

Question

Two identical containers are filled to the same height, one with water and the other with mercury. Which container experiences a greater pressure at the bottom?

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Hydrostatic Pressure
 **Related Topics**: Density, Fluid Mechanics
 **Prerequisites**: Understanding of pressure and density.
## SOLUTION PATHWAY
**Given Information**:
  Two identical containers filled to the same height.
  One container filled with water.
  One container filled with mercury.
  Height of water column = Height of mercury column.
**Method & Steps**:
 1. Determine the formula for hydrostatic pressure.
  Reasoning: Hydrostatic pressure is the pressure exerted by a fluid at rest due to gravity.
  Formula/Rule: $P = ρgh$, where:
   *  $P$ is the pressure
   *  $ρ$ is the density of the fluid
   *  $g$ is the acceleration due to gravity
   *  $h$ is the height of the fluid column
 2. Compare the densities of water and mercury.
  Working: The density of mercury (ρ_mercury) is significantly greater than the density of water (ρ_water).  (ρ_mercury ≈ 13600 kg/m³, ρ_water ≈ 1000 kg/m³)
  Key Point:  Since the height (h) and gravity (g) are the same for both containers, the pressure difference is solely dependent on the density (ρ).
 3. Calculate and compare the pressures.
  Result: Since ρ_mercury > ρ_water, and h and g are constant, the pressure at the bottom of the container with mercury ($P_{mercury} = ρ_{mercury}gh$) will be greater than the pressure at the bottom of the container with water ($P_{water} = ρ_{water}gh$).
  Verification: The calculation directly shows that the mercury column exerts a much higher pressure due to its higher density.
 ## OPTION ANALYSIS
A :x: The container with water has lower pressure due to lower density of water.
B ✓: The container with mercury has higher pressure due to the higher density of mercury.
C :x:  The pressures are different because the densities of water and mercury are different.
D :x: The container shape is irrelevant; only height, density, and gravity affect the pressure at the bottom.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Ignoring the density difference: Students might assume pressure depends only on height, neglecting the crucial role of density.
   How to avoid: Always remember that hydrostatic pressure is directly proportional to both density and height.
  2.Confusing pressure and force: Pressure is force per unit area.  While the force exerted by the mercury column is greater, the question asks about pressure.
   How to avoid: Clearly understand the difference between pressure and force.
 **Quick Tips**:
  1.Remember the formula $P = ρgh$ and its implications.
  2.Memorize that mercury is much denser than water.

SUBHANI · Answer

The container with water

SUBHANI · Answer

The correct Option is "The container with mercury"

SUBHANI · Answer

Both containers experience the same pressure

SUBHANI · Answer

Pressure cannot be determined without knowing the container shape

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