find the dimensitions of coefficient of viscocity and its SI unit .

According to Stoke's Law, a body of radius r moving with velocity v through a medium of coefficient of viscosity η experiences a viscous force given by:

F = 6πηrv

η = F / (6πrv)  …… …… ……… …...(i)

Now, dimension of force (F)  =  [M¹ L¹ T^-2]

dimensions of radius (r) = [L¹]

dimensions of velocity (v) = [L¹ T^-1]

6π is a dimensionless factor

therefore, dimensions of coefficient of viscosity (η) = [M¹ L¹ T^-2] / [L¹] [L¹ T^-1]

………  …………………  ……………………  ....... ...........= [M¹ L^-1 T^-1]

From the dimensional formula, the SI unit of coefficient of viscosity (η) is  kg m^-1 s^-1