Question

A long cylindrical rod of radius $R_1$ is placed co-axially inside a cylindrical tube of radius $R_2(>R_1)$ filled withviscous liquid and pulled along the axis with a constant velocity. In steady state the velocity gradient $\left(\frac{dv}{dr}\right)$ depends on the distance from the common axis 'r' as proportional to

• A. $r^{\circ }$
• B. $r^{-1}$
• C. $r^{-2}$
• D. $r^{-3}$

Answer 1

The correct option is B

$r^{-1}$

$f=\eta A\frac{dv}{dx}=const\eta 2\pi rl\frac{dv}{dx}=const\frac{dv}{dx}\alpha \frac{1}{r}$