A small spherical ball of radius r falls with velocity `upsilon` through a liquid having coeffiecinet of viscosity `eta.` find viscous darg F on the wall if it depends or `r, upsilon, eta. Take K = 6 pi`

Answer

`F = K r upsilon eta`

Explanation

Let `F = K r^a upsilon^b eta^c ….(i)`
Where K is dimensionles constant of
proportionality.
`[M^1L^1 T^(-2)]= L^a(LT^(-1))^b (ML^(-1)) T^(-1)c]`
`=M^c L^(a+b-c) T^(-b-c)`
Applying the principle of homogeneity of dimensions, we get
c=1, a+b -c =1 ...(ii)
-b-c =-2 ….(iii)`
From (iii), -b -1 = -2, or -b = +1-2 =-1,
From (ii), a + 1 -1 =1, or a= 1`
Putting these values in (i) we get
`F = K r^1 upsilon^1 eta^1`