Given that MLT is the dimension of pressure, what are the values?

Understand the Problem

The question is asking about the values associated with the dimension of pressure in terms of mass (M), length (L), and time (T). To solve this, we need to express pressure in its fundamental dimensions.

Answer

$[P] = M L^{-1} T^{-2}$

Steps to Solve

Define Pressure in Terms of Force and Area

Pressure ($P$) is defined as force ($F$) applied over an area ($A$). Therefore, we can express pressure mathematically as: $$ P = \frac{F}{A} $$

Break Down Force into Fundamental Dimensions

Force is defined by Newton's second law, which states that force is mass times acceleration. The equation for force is given by: $$ F = m \cdot a $$ Here, $m$ is mass and $a$ is acceleration. Acceleration can be expressed in fundamental dimensions as: $$ a = \frac{L}{T^2} $$ So, we can substitute this into the force equation: $$ F = m \cdot \frac{L}{T^2} $$

Calculate the Dimensions of Area

The area ($A$) is defined as length squared: $$ A = L^2 $$

Substituting into the Pressure Formula

Now, substituting the expressions for force and area back into the pressure formula: $$ P = \frac{F}{A} = \frac{m \cdot \frac{L}{T^2}}{L^2} $$

Simplifying the Expression

This simplifies to: $$ P = \frac{m}{L \cdot T^2} $$

Final Representation of Pressure in Fundamental Dimensions

Thus, the dimensions of pressure can be expressed as: $$ [P] = M L^{-1} T^{-2} $$

The dimension of pressure is given by $[P] = M L^{-1} T^{-2}$.

More Information

Pressure is an important concept in physics and engineering, commonly associated with fluids, gases, and solid mechanics. It is measured in units such as Pascals (Pa) in the International System of Units (SI).

Tips

One common mistake is confusing pressure with force; they are related but not the same. Remember that pressure involves division by area, while force involves mass and acceleration directly.

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