Question

Two physical quantities having the same dimensional formula \( [M^1 L^{-1} T^{-2}] \) are

• A. Thrust and Strain
• B. Moment of force and Thrust
• C. Stress and Pressure
• D. Work and thrust

Hint:

Whenever two quantities are defined using the same formula (like force/area), their dimensional formulas will be identical.

Answer 1

The Correct Option is C

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

Step 2: Write dimensional formula of stress.
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]
\[ = [ML^{-1}T^{-2}] \]

Step 3: Check other options.
Thrust \(=\) Force \(=[MLT^{-2}]\) (not matching)
Strain \(=\) dimensionless
Moment of force \(=[ML^2T^{-2}]\)
Work \(=[ML^2T^{-2}]\)

Step 4: Identify matching pair.
Only stress and pressure have same dimensional formula.

Step 5: Concept understanding.
Both are defined as force per unit area.

Step 6: Conclusion.
Thus, they share identical dimensions.

Step 7: Final answer.
\[ \boxed{\text{Stress and Pressure}} \]