In this post we will solve Numerical problems on Terminal Velocity. Here is the first set.

## Numerical problem on Terminal Velocity with solution

**1 ) Find the terminal velocity of (a) a steel ball bearing of radius 1 mm and (b) a steel ball bearing of radius 2 mm falling through glycerine in a cylinder. **

The viscosity of glycerine 1.5 Pa s. (at 20 degree C)

Density of steel = 7800 kg/m^3

Density of glycerine = 1200 kg/m^3

g = 9.81 m/s^2

**Solution:**

**(a) for 1 mm radius ball bearing:****V _{term} **= [2 r

^{2}g (ρ

_{s}– ρ

_{f})] / [9Ƞ]

= [2(1×10

^{-3})

^{2}x 9.81 X (7800-1200)]/[9×1.5] =

**9.6 x 10**

^{-3}ms^{-1}**(b) for 2 mm radius ball bearing:****V _{term}** = [2 r

^{2}g (ρ

_{s}– ρ

_{f})] / [9Ƞ]

= [2(2×10

^{-3})

^{2}x 9.81 X (7800-1200)]/[9×1.5] =

**3.8 x 10**

^{-2}ms^{-1}**Reference:**

Derivation of Terminal Velocity (step by step)

Stokes’ Law | drag force Formula