Question

Two small spheres of radii $r$ and $ 4r $ fall through a viscous liquid with the same terminal velocity. The ratio between the viscous forces acting on them is

• A. $ 1:2 $
• B. $ 4:1 $
• C. $ 1:16 $
• D. $ 1:4 $

Answer 1

Answer: (D)

The magnitude of the viscous force depends on the shape and size of the body, its speed and the viscosity of the fluid. Stokes established that if a sphere of radius $r$ moves with velocity $v$ through a fluid of viscosity $\eta$, the viscous force opposing the motion of the sphere
$ F=6\pi \eta rv $
$ \frac{F_{1}}{F_{2}}=\frac{r_{1}}{r_{2}} $
[As $ \eta = $ constant and $ v_{1}=v_{2} $ ]
$ \frac{F_{1}}{F_{2}}=\frac{r}{4r} $