Question

The physical quantity that does not have the dimensional formula \( [ML^{-1}T^{-2}] \) is

• A. force
• B. pressure
• C. stress
• D. modulus of elasticity
• E. energy density

Hint:

Quantities like pressure, stress, modulus, and energy density often share the same dimensions because they are ratios involving force and area or energy and volume.

Answer 1

The Correct Option is A

Concept: Dimensional formula represents the dependence of a physical quantity on fundamental quantities like mass (M), length (L), and time (T). Many physical quantities like pressure, stress, modulus, and energy density share the same dimensional formula because they are defined as force per unit area or energy per unit volume.

Step 1: Write dimensional formula of force. \[ \text{Force} = ma \Rightarrow [M][LT^{-2}] = [MLT^{-2}] \]

Step 2: Check dimensional formula of pressure. \[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}] \]

Step 3: Check stress and modulus of elasticity. \[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \Rightarrow [ML^{-1}T^{-2}] \] \[ \text{Modulus} = \frac{\text{Stress}}{\text{Strain}} \Rightarrow [ML^{-1}T^{-2}] \]

Step 4: Check energy density. \[ \text{Energy density} = \frac{\text{Energy}}{\text{Volume}} = \frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}] \]

Step 5: Conclusion. Only force has dimensional formula \( [MLT^{-2}] \), not \( [ML^{-1}T^{-2}] \).