Question

Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given $\eta =\frac{p(r^2-x^2)}{4vl}$, where v is velocity of oil at a distance x from the axis of the tube. The dimensional formula of viscosity is

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^1{L}^{-1}{T}^{-1}\right]$
• C. $\left[M{L}^2{T}^{-1}\right]$
• D. $\left[M^{-1}{L}^{-1}{T}^1\right]$

Answer 1

The correct option is B $\left[M^1{L}^{-1}{T}^{-1}\right]$

Dimensions of $P=\left[M{L}^{-1}{T}^{-2}\right]$

Dimentions of $r=\left[L\right]$

Dimentions of $v=\left[L{T}^{-1}\right]$

Dimensions of $I=\left[L\right]$

$\eta =\frac{p(r^2-x^2)}{4vl}$

$=\frac{\left[M{L}^{-1}{T}^{-2}\right]\left[L^2\right]}{\left[L{T}^{-1}\right]\left[L\right]}$

$=\left[M{L}^{-1}{T}^{-1}\right]$