Question

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

• A. mass
• B. length
• C. time
• D. none of the above

Answer 1

The correct option is A mass

$F=\mu A\frac{u}{y}⟹\mu =\frac{Fy}{uA}$

$F=$ Force

Dimensions are $\left[ML{T}^{-2}\right]$

$u=$ Speed

Dimensions are $\left[L{T}^{-1}\right]$

$y=$ Distance

Dimensions are $\left[L\right]$

$\mu =$ coefficient of viscosity

$A=$ area of the cross section.

Dimensions are $\left[L^2\right]$

Dimensions for coefficient of viscosity will be $\frac{\left[{MLT}^{-2}\right]\ast \left[L\right]}{{[LT}^{-1}]\ast [L^2]}=\left[M{L}^{-1}{T}^{-1}\right]$

Tension is a force used in a different context.

Dimensions are $\left[ML{T}^{-2}\right]$

Only mass has same power in both viscosity and tension.