C

Step 1: First, we need to understand the definition of pressure. Pressure is defined as force per unit area. The formula for pressure (P) can be expressed as: $$ P = \frac{F}{A} $$ where: - $F$ is the force applied (in Newtons) - $A$ is the area (in square meters)
Step 2: The dimensional formula of force ($F$) is: $$ [F] = [M][L][T^{-2}] $$ This can be derived from Newton’s second law, where force is the product of mass and acceleration.
Step 3: The dimensional formula for area ($A$) is: $$ [A] = [L^2] $$ Now, substituting this into the pressure formula gives:
Step 4: Substitute the dimensions into the pressure formula: $$ [P] = \frac{[F]}{[A]} = \frac{[M][L][T^{-2}]}{[L^2]} $$ This simplifies to: $$ [P] = [M][L^{-1}][T^{-2}] $$
Conclusion: This means that the dimensions of pressure are represented as: $$ M L^{-1} T^{-2} $$ This corresponds to option C, which is effectively represented like this:
Therefore, the correct answer is C.