Question

Of the following, the pair of physical quantities not having the same dimensional formula is:

• A. Work and torque
• B. Angular momentum and Planck's constant
• C. Stress and linear momentum
• D. Surface tension and force constant

Hint:

For dimensional analysis, express the physical quantity in terms of fundamental units: \[ M \rightarrow \text{Mass}, L \rightarrow \text{Length}, T \rightarrow \text{Time} \] Matching dimensions verifies equivalent physical quantities.

Answer 1

The Correct Option is C

Step 1: Dimensional Analysis 1. Work and Torque - Work: \( [ML^2T^{-2}] \) - Torque: \( [ML^2T^{-2}] \) - Same dimensional formula. 2. Angular Momentum and Planck’s Constant - Angular Momentum: \( [ML^2T^{-1}] \) - Planck’s Constant: \( [ML^2T^{-1}] \) - Same dimensional formula. 3. Stress and Linear Momentum - Stress: \( [ML^{-1}T^{-2}] \) - Linear Momentum: \( [MLT^{-1}] \) - Different dimensional formula. 4. Surface Tension and Force Constant - Surface Tension: \( [MT^{-2}] \) - Force Constant: \( [MT^{-2}] \) - Same dimensional formula. Conclusion: Stress and linear momentum do not share the same dimensional formula. Thus, the correct answer is: \[ \text{Stress and linear momentum} \]