When a solid moves through a liquid, the liquid opposes the motion with a force F. The magnitude of F depends on the coefficient of viscosity `eta` of the liquid, the radius r of the sphere and the speed v of the sphere. Assuming that F is proportional to different powers of these quantities, guess a formula for F using the method of dimension.

Explanation

Suppose the formula is `F=k eta ^(a) r^(b) v^(c)`
Then , `MLT^(-2) = [ML^(-1)T^(-1)]^(a)L^(b) ((L)/(T))^(c)`
`=M^(a)L^(-a+b+c) T^(-a-c)`
Equating the exponents of M, L and T from both sides,
`a=1`
`- a + b + c = 1`
`- a -b = - 2`
Solving these, `a = 1 ,b = 1 and c = 1 `
Thus , the formula for F is `F=k eta r v` .