The dimensional formula of coefficient of viscosity is

Options

A. Dimensional formula: `[M^(1)L^(-1)T^(-1)]`
B. Dimensional formula: `[M^(2)L^(-3)T^(-1)]`
C. Dimensional formula: `[M^(-4)L^(1)T^(-2)]`
D. Dimensional formula: `[M^(-1)L^(3)T^(-2)]`

Answer

A

Explanation

Coefficient of viscosity `(eta) = (Fx)/(Av)`
F = tangential Force,
A = Area, x = distance between the layers, v = velocity.
Dimensional Formula of Force = `M^(1)L^(1)T^(-2)`
Dimensional Formula of Area = `M^(@)L^(2)T^(@)`
Dimensional Formula of distance = `M^(@)L^(1)T^(@)`
Dimensional Formula of velocity = `M^(@)L^(1)T^(-1)`
Putting these values in above equation we get,
`[eta] = ([M^(1)L^(1)T^(-2)][M^(@)L^(1)T^(@)])/([M^(@)L^(2)T^(@)][M^(@)L^(1)T^(-1)]) = [M^(1)L^(-1)T^(-1)]`