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Fluid Mechanics - Engineering

Q1:

The dimension of surface tension is

A ML-2

B MT-2

C MLT-2

D ML-2T

ANS:B - MT-2

Surface tension is defined as the force acting per unit length along the interface between two liquids or between a liquid and a gas. Its dimensional formula can be derived using Newton's equation: γ=FL\gamma = \frac{F}{L}γ=LF​ where γ\gammaγ is surface tension, FFF is force, and LLL is length. To find the dimensions:

  • The dimension of force [F][F][F] is MLT−2\text{MLT}^{-2}MLT−2.
  • The dimension of length [L][L][L] is L\text{L}L.
Therefore, the dimensional formula for surface tension [γ][\gamma][γ] is: [γ]=[F][L]=MLT−2L=MT−2[\gamma] = \frac{[F]}{[L]} = \frac{\text{MLT}^{-2}}{\text{L}} = \text{MT}^{-2}[γ]=[L][F]​=LMLT−2​=MT−2 So, the correct answer is: MT−2^{-2}−2