Question

The fundamental unit which has the same power in the dimensional formula of surface tension and coefficient of viscosity is:

• A. mass
• B. length
• C. time
• D. none

Answer 1

Answer: (A)

mass

Surface tension $=\frac{F}{l}=\frac{M^1{L}^1{T}^{-2}}{L^1}=M^1{T}^{-2}$
Coeff of viscosity $=\frac{k}{qA\frac{dv}{dz}}=\frac{M^1{L}^1{T}^{-2}}{\frac{L^{2}L{T}^{-1}}{L}}=M^1{L}^{-1}{T}^{-1}$
Hence, mass has the same power.