The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 ~cm / s . The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be \_\_\_\_ cm / s .

Question

Quantrex Academy · Accepted Answer

Correct answer: 5

For a sphere in a viscous fluid, terminal velocity is proportional to

r^2

:

v_t \propto r^2

.
For two balls of the same material in the same fluid:

\frac{v_{t1}}{v_{t2}} = \frac{r_1^2}{r_2^2}

.
Given

r_1 = 6

mm,

v_{t1} = 20

cm/s, and

r_2 = 3

mm:

\frac{20}{v_{t2}} = \frac{36}{9} = 4

.
Therefore,

v_{t2} = 5

cm/s.

The terminal velocity of a metallic ball of radius 6 mm in a...

Correct answer

Step-by-step solution

More from Mechanical Properties of Fluids