Q. Which of the following pairs does not have similar dimensions?
NTA AbhyasNTA Abhyas 2022
Solution:
Tension will have dimensions of force and surface tension will have dimension of force per unit length, so they have different dimensions.
[Tension] $=\left[\right.$ Force $\left]\right.=MLT^{- 2}$
Surface tension $=\frac{\text{ Force }}{\text{ length }}=\frac{MLT^{- 2}}{L}=ML^{0}T^{- 2}$
Stress and pressure has same unit i.e., $Newtonmetre^{- 2}$ .
The dimension of Planck's constant is equal with the dimension of angular momentum i.e., $ML^{2}T^{- 1}$ .
Angle and strain have no unit.
[Tension] $=\left[\right.$ Force $\left]\right.=MLT^{- 2}$
Surface tension $=\frac{\text{ Force }}{\text{ length }}=\frac{MLT^{- 2}}{L}=ML^{0}T^{- 2}$
Stress and pressure has same unit i.e., $Newtonmetre^{- 2}$ .
The dimension of Planck's constant is equal with the dimension of angular momentum i.e., $ML^{2}T^{- 1}$ .
Angle and strain have no unit.