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 the coil is given by `eta = (p (r^(2) - x^(2)))/(4 vL)`, where `v` is the velocity of oil at a distance `x` from the axis of the tube. From this relation, the dimensions of viscosity `eta` are

Options

A. `[M^(0)L^(0)T^(0)]`
B. `[MLT^(-1)]`
C. `[ML^(2)T^(-2)]`
D. `[ML^(-1)T^(-1)]`

Answer

D

Explanation

Pressure `(p) = ("Force")/("Area") = ([MLT^(-2)])/([L^(2)]) = [ML^(-1)T^(-2)]`
Velocity, `v = [LT^(-1)]`
From principle of homogeneity, the dimensions of `r^(2)` and `x^(2)` are same. So, the dimensions of viscosity,
`eta = ([ML^(-1)T^(-2)][L^(2)])/([LT^(-1)][L])`
`= [ML^(-1)T^(-1)]`