Question

The pair of physical quantities not having same dimensions is:

• A. Torque and energy
• B. Pressure and Young's modulus
• C. Angular momentum and Planck's constant
• D. Surface tension and impulse

Hint:

When checking if two physical quantities have the same dimensions, write down their dimensional formulas and compare them. If they are the same, the quantities have the same dimensions.

Answer 1

The Correct Option is A

- Torque is given by \( {Torque} = {Force} \times {Distance} \), so its dimensional formula is \( [M L^2 T^{-2}] \). 
- Energy is given by \( {Energy} = {Force} \times {Distance} \), so its dimensional formula is also \( [M L^2 T^{-2}] \). Hence, Torque and Energy have the same dimensions, and the correct answer is not option (1). Let's check other options to make sure. 
- Pressure is given by \( {Pressure} = \frac{{Force}}{{Area}} \), so its dimensional formula is \( [M L^{-1} T^{-2}] \). 
- Young’s modulus is given by \( {Young's modulus} = \frac{{Stress}}{{Strain}} \), and its dimensional formula is also \( [M L^{-1} T^{-2}] \). Thus, Pressure and Young’s modulus have the same dimensions. 
- Angular momentum has dimensions \( [M L^2 T^{-1}] \) and Planck's constant has dimensions \( [M L^2 T^{-1}] \), so they have the same dimensions. 
- Surface tension has dimensions \( [M T^{-2}] \) and impulse has dimensions \( [M L T^{-1}] \), so they do not have the same dimensions. Thus, the correct answer is option (1).