Solution:
Coefficient of viscosity η =2.42Ns/m2
Density of the steel ρs= 7800kg/m3
Density of the castor oil ρc= 940kg/m3
radius of the steel ball (r)=2 *10-3 mm
When he balls falls with the terminal velocity
Weight of the ball = viscous force + upthrust
$6\pi \eta r{v_t} + \frac{{4\pi }}{5}{r^3}g{\rho _c} = {\rm{
}}\frac{{4\pi }}{5}{r^3}g{\rho _s}$
Where vt is the terminal velocity of the
ball
$\therefore {\rm{ }}{v_t} = {\rm{
}}\frac{{\frac{2}{9}{r^2}g({\rho _c} - {\rho _s})}}{\eta }$
= 0.25m/s