Question

Dimensions of stress are:

• A. $ [MLT^{-2}]$
• B. $ [ML^2T^{-2}]$
• C. $ [M^1L^{-1}T^{-2}]$
• D. $ [ML^{-2} T^{-2}]$

Answer 1

The Correct Option is C

To determine the dimensions of stress, we need to understand what stress represents in physics. Stress is defined as the force applied per unit area. Mathematically, stress can be expressed as:

\(Stress = \frac{Force}{Area}\)

Now, let's break down the dimensions for both force and area:

1. Dimensions of Force: Force is defined as mass times acceleration. Therefore, the dimensions of force are: \([F] = [M^1L^1T^{-2}]\).
2. Dimensions of Area: Area is a measure of space in two dimensions (length squared). Thus, the dimensions of area are: \([A] = [L^2]\).

Substituting these into the formula for stress, we have:

\(Stress = \frac{[F]}{[A]} = \frac{[M^1L^1T^{-2}]}{[L^2]}\)

By simplifying, we find:

\([Stress] = [M^1L^{-1}T^{-2}]\)

Therefore, the correct dimensional formula for stress is \([M^1L^{-1}T^{-2}]\), which matches the given correct answer.

Let's review why the other options are incorrect:

• \([MLT^{-2}]\): These are the dimensions for force, not stress.
• \([ML^2T^{-2}]\): These dimensions describe energy or work, not stress.
• \([ML^{-2}T^{-2}]\): While similar, these dimensions do not correctly represent stress as the exponent of \(L\) is off by 1.

In summary, understanding and applying the formula for stress allows us to deduce the correct dimensional formula, confirming that the correct option is indeed \([M^1L^{-1}T^{-2}]\).