Question

The pair of physical quantities not having the 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:

Ensure you are familiar with the dimensional analysis of physical quantities to determine whether pairs of quantities share the same dimensions.

Answer 1

The Correct Option is A

- Torque has the dimension \( [M L^2 T^{-2}] \), and energy also has the dimension \( [M L^2 T^{-2}] \), so they have the same dimension.
- Pressure has the dimension \( [M L^{-1} T^{-2}] \), and Young’s modulus has the same dimension \( [M L^{-1} T^{-2}] \).
- Angular momentum has the dimension \( [M L^2 T^{-1}] \), and Planck’s constant also has the dimension \( [M L^2 T^{-1}] \).
- Surface tension has the dimension \( [M T^{-2}] \), while impulse has the dimension \( [M L T^{-1}] \), so they do not have the same dimensions.