The Question is from neet-physics mechanical-properties-of-fluids variation-of-pressure-upthrust, and it was created by the author NAGA SAI

Question

A solid cube of side 10 cm is immersed in water. The pressure on the top face of the cube is $P_1$ and on the bottom face is $P_2$. If the density of water is $1000 \ kg/m^3$ and $g = 10 \ m/s^2$, what is the difference in pressure, $P_2 - P_1$?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Hydrostatic pressure
 **Related Topics**: Fluid mechanics, pressure difference in fluids
 **Prerequisites**: Understanding of pressure, density, and hydrostatic pressure formula.
## SOLUTION PATHWAY
**Given Information**:
  Side of cube, $s = 10 	ext{ cm} = 0.1 	ext{ m}$ 
  Density of water, $ho = 1000 	ext{ kg/m}^3$
  Acceleration due to gravity, $g = 10 	ext{ m/s}^2$
  Pressure at top face = $P_1$
  Pressure at bottom face = $P_2$
**Method & Steps**:
 1. Calculate the pressure difference using the hydrostatic pressure formula.
  Reasoning: The pressure difference between two points in a fluid is given by the product of the fluid density, acceleration due to gravity, and the vertical distance between the points.
  Formula/Rule: $\Delta P = ho g h$, where $\Delta P$ is the pressure difference, $ho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the vertical distance.
 2. Determine the vertical distance between the top and bottom faces of the cube.
  Working: The vertical distance $h$ is equal to the side length of the cube, which is 0.1 m.
  Key Point: The pressure increases linearly with depth in a fluid.
 3. Substitute the values into the formula and calculate the pressure difference.
  Result: $\Delta P = P_2 - P_1 = (1000 	ext{ kg/m}^3)(10 	ext{ m/s}^2)(0.1 	ext{ m}) = 1000 	ext{ Pa}$ 
  Verification: The units are consistent (kg m/s²/m² = Pa), and the magnitude is reasonable for a pressure difference in water at a depth of 10 cm.
 ## OPTION ANALYSIS
A :x: 100 Pa is incorrect. It is an order of magnitude too small.
B :x: 1000 Pa is the correct pressure difference.
 C ✓: 10000 Pa is incorrect. This would be the pressure difference if the height was 1 meter.
D :x: 1 Pa is far too small.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Using incorrect units: Ensure all units are consistent (SI units are recommended).
  2.Forgetting to convert units: Convert centimeters to meters before calculation.
 **Quick Tips**:
  1.Remember the formula $\Delta P = ho g h$.
  2.Visualize the pressure increasing with depth in the fluid.

NAGA SAI · Answer

100 Pa

NAGA SAI · Answer

The correct Option is "1000 Pa"

NAGA SAI · Answer

10000 Pa

NAGA SAI · Answer

1 Pa

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