Question

$Asmallsphericalbodyofmassmandradiusrfallswithvelocity\text{'}v\text{'}havingcoefficientofvis\cos ity\eta .FindtheviscousforceFifitdepensonalloftheabove.$

Answer 1

Dear Student,
​Suppose a spherical body of radius r moves at speed v through a fluid of viscosity ƞ ,viscous force F acting on the body depends on r,v and ƞ .
According to the dimensional analysis we can write,

Let F = kr^av^b ƞ^​c

Where k is the dimensional less constant.

MLT^-2 = kL^a(LT^-1)^b(ML^-1 T^-1)^c

On equating the coefficients of M,L,T on both sides we get :
a,b,c each = 1
hence F = krvƞ,
value of k = 6π,
hence stokes law becomes,

F = 6πƞrv

This is the required viscous force

Regards