Turpentine oil is flowing through a tube of length I and radius r. The pressure difference between the two ends of the tube is P , the visocity of oil at a distance x from the axis of tube from this relation, the dimensions of viscosity 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

Here length = I[L], radius = r[L],
Pressure difference =` P [ML^(-1) T^(-2)]`,
velocity `=upsilon[LT^(-1)]`
distance from the exist of tube = x [L]
As eta = `(p(r^2 - x^2))/(4 upsilonI)`, :. eta = `(ML^(-1)T^(-2)[L^2])/(LT^(-1).L)`
`[:. r^2 -x^2 = L^2 - L^2 = L^2]`
`eta = [ML^(-1)T^(-1)]`