What is the SI unit of pressure? A. Newton per square centimetre (Newton per square centimetre) B. Newton - Square Meter (Newton - Square Meter) C. Newton per square meter (Newton per square meter) D. Newton - Square centimetre (Newton - Square centimetre)
C
Understanding the SI Unit of Pressure
Pressure is a fundamental physical quantity that describes the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It's commonly encountered in various fields, from physics and engineering to everyday life, such as measuring atmospheric pressure or tire pressure.
Mathematically, pressure (\(P\)) is defined as:
\(P = \frac{\text{Force}}{\text{Area}}\)
To determine the SI unit of pressure, we need to use the SI units for force and area.
SI Units for Force and Area
- The SI unit of force is the Newton (N). A Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
- The SI unit of length is the meter (m). Consequently, the SI unit of area, which is derived from length squared, is the square meter (m\(^2\)).
Deriving the SI Unit of Pressure
Using the formula for pressure and the SI units for force and area, we can derive the SI unit for pressure:
SI unit of Pressure = \(\frac{\text{SI unit of Force}}{\text{SI unit of Area}}\) = \(\frac{\text{Newton}}{\text{square meter}}\)
Thus, the SI unit of pressure is Newton per square meter (N/m\(^2\)). This derived unit is also given a special name: the Pascal (Pa). So, 1 Pa = 1 N/m\(^2\).
Analyzing the Given Options
Let's examine the provided options in light of our understanding of the SI unit of pressure:
| Option | Unit | Analysis |
|---|---|---|
| A | Newton per square centimetre (Newton per square centimetre) | Square centimeter (cm\(^2\)) is a unit of area, but it is not the SI base unit. The SI unit for length is meter, making the SI unit for area square meter (m\(^2\)). |
| B | Newton - Square Meter (Newton - Square Meter) | This represents the product of Newton and square meter (N ⋅ m\(^2\)), which is not the unit of pressure. Pressure is force per area. |
| C | Newton per square meter (Newton per square meter) | This unit, N/m\(^2\), is derived directly from the SI units of force (Newton) and area (square meter). This is the correct SI unit for pressure, also known as the Pascal (Pa). |
| D | Newton - Square centimetre (Newton - Square centimetre) | This represents the product of Newton and square centimeter (N ⋅ cm\(^2\)) and uses a non-SI unit for area. It is not the unit of pressure. |
Based on this analysis, the correct SI unit of pressure is Newton per square meter.
Revision Table: Pressure Units
| Quantity | Formula | SI Unit | Common Symbol | Notes |
|---|---|---|---|---|
| Pressure | \(P = F/A\) | Newton per square meter | N/m\(^2\) or Pa (Pascal) | Pascal (Pa) is the special name for N/m\(^2\). |
| Force | - | Newton | N | Base unit derived from kg, m, s. |
| Area | - | Square meter | m\(^2\) | Derived from the SI unit of length (meter). |
Additional Information on Pressure and Units
While Pascal (Pa) or Newton per square meter (N/m\(^2\)) is the SI unit, pressure is often measured in other units depending on the application. Some common non-SI units of pressure include:
- Atmosphere (atm): Represents the average atmospheric pressure at sea level. \(1 \text{ atm} \approx 101325 \text{ Pa}\).
- Bar: Commonly used in meteorology. \(1 \text{ bar} = 100000 \text{ Pa}\).
- Pounds per square inch (psi): Widely used in the United States, especially for tire pressure and hydraulic systems.
- Millimeters of mercury (mmHg) or Torr: Used in medicine (blood pressure) and vacuum measurements. \(1 \text{ Torr} = 1 \text{ mmHg} \approx 133.322 \text{ Pa}\).
Understanding the relationship between force, area, and pressure is crucial. For a constant force, increasing the area over which the force is applied decreases the pressure, and decreasing the area increases the pressure. This principle explains why sharp objects (small area) exert high pressure and can cut, while flat objects (large area) exert lower pressure.
Important Questions from Units and Dimensional Formula
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