COMEDK · Physics · 2. Units and Dimensions

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

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

Verified Solution

Answer & Solution

Correct Answer

(D) Stress and Pressure

Step-by-step Solution

Detailed explanation

The dimensional formula for Stress is \(\dfrac{\text{Force}}{\text{Area}} = \dfrac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]\). The dimensional formula for Pressure is \(\dfrac{\text{Force}}{\text{Area}} = \dfrac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]\). Since both…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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