What is Stoke's law ? Find an expression for it.

Explanation

According to Stoke.s law
If F = Viscous drag acting on the spherical body
r = Radius of spherical body
v = Terminal velocity of the body
`eta=` coefficient of viscosity
then, `F=6pietarv`.
This law can be proved by using the method of dimensional analysis. As the viscous drag (F) acting on the sphere depends upon
i) the radius of the sphere (r)
ii) terminal velocity (v) and
iii) coefficient of viscosity `(eta)` i.e., `F=Kr^(a)v^(b)eta^(c)" "........(i)`
Where K is a dimensionless constant.
The dimensional formulae of various quantities are,
`[F]=MLT^(-2)," "[r]=L,`
`[v]=LT^(-1)," "[eta]=ML^(-1)T^(-1)`
Substituting in equation (i), we get
`[MLT^(-2)]=[L]^(a)[LT^(-1)]^(b)[ML^(-1)T^(-1)]^(c)=[M^(c)L^(a+b+c)T^(-b-c)]`
Comparing powers of M, L and T on both the sides, we get
`c=1" ".......(ii)`
`a+b-c=1" "........(iii)`
`-b-c=-2" "..........(iv)`
Using equation (ii) in (iv), we get b=1
Using b=1 and c= 1 in (iit), we get a = 1
Substituting values of a, b and c in (1), we get
`F=Krveta`
Value of `K=6pi` (found numerically)
Therefore, `F=6pietarv`
This Stoke.s law.