Question

Which of the following pairs does not have similar dimensions?

• A. Tension and surface tension
• B. Stress and pressure
• C. Planck’s constant and angular momentum
• D. Angle and strain

Answer 1

Answer: (A)

Tension will have dimensions of force and surface tension will have dimension of force per unit length, so they have different dimensions.
[Tension] $=[$ Force $]=ML{T}^{-2}$
Surface tension $=\frac{\text{ Force }}{\text{ length }}=\frac{ML{T}^{-2}}{L}=M{L}^0{T}^{-2}$
Stress and pressure has same unit i.e., $Newtonmetr{e}^{-2}$ .
The dimension of Planck's constant is equal with the dimension of angular momentum i.e., $M{L}^2{T}^{-1}$ .
Angle and strain have no unit.