Question

Which of the following pairs have different dimensions?
Given that angular velocity is angle/time and surface tension is force/length.

• A. Frequency and angular velocity
• B. Tension and surface tension
• C. Mass density and energy density
• D. Speed and velocity

Answer 1

Answer: (B), (C)

The correct options are
B Tension and surface tension
C Mass density and energy density

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 $\left(\frac{\text{energy}}{\text{volume}}\right)$.