First slide

Viscous flow/Laminar flow

Question

A small steel ball of radius r experiences a viscous force F when it is falling in a jar of glycerine with terminal velocity v. The viscons force experienced by a steel ball of radius r/2 falling in glycerine with terminal velocity v/2 is

Moderate

A

F
B

$\frac{F}{2}$
C

$\frac{F}{4}$
D

$\frac{F}{8}$

Solution

$\begin{array}{l} F = 6 πηrv \\ F^{'} = 6 πη (\frac{r}{2}) \times (\frac{v}{2}) = \frac{1}{4} \times 6 πηrv = \frac{F}{4} \end{array}$
So the correct choice is (c).

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