Question

Which of the following pairs have different dimensions? (Given: surface tension is energy/area)

• A. Frequency and angular velocity
• B. Tension and surface tension
• C. Density and energy density
• D. Linear momentum and angular momentum

Answer 1

Answer: (B), (C), (D)

Linear momentum and angular momentum

Frequency and angular velocity have same dimensions $\left[T^{-1}\right]$.
Tension has dimension of force and surface tension has dimension of (force/length). Density has dimensions $\left(\frac{\text{mass}}{\text{volume}}\right)$ and energy density has dimensions $\left(\frac{\text{energy}}{\text{volume}}\right)$. Angular momentum has dimensions of (linear momentum $\times$ distance).