Physics - Fluid Question with Solution | TestHub

When the spherical ball attains constant (terminal) velocity, the net force acting on it is zero. The downward weight of the ball is balanced by the upward buoyant force and the viscous force.

Viscous force $F_v=W-F_B$

$F_v=\frac{4}{3}\pi r^3\rho g-\frac{4}{3}\pi r^3\sigma g$

$F_v=\frac{4}{3}\pi r^3(\rho -\sigma )g$

Given values in SI units:
$r=1\text{ mm}=10^{-3}\text{ m}$
$\rho =10.5\text{ g/cc}=10.5\times 10^3{\text{ kg/m}}^3$
$\sigma =1.5\text{ g/cc}=1.5\times 10^3{\text{ kg/m}}^3$
$g=9.8{\text{ m/s}}^2$

Substituting the values:

$F_v=\frac{4}{3}\times \frac{22}{7}\times (10^{-3}{)}^3\times (10.5\times 10^3-1.5\times 10^3)\times 9.8$

$F_v=\frac{4}{3}\times \frac{22}{7}\times 10^{-9}\times 9000\times 9.8$

$F_v=4\times 22\times 3000\times \frac{9.8}{7}\times 10^{-9}$

$F_v=88\times 3000\times 1.4\times 10^{-9}$

$F_v=88\times 4200\times 10^{-9}$

$F_v=369600\times 10^{-9}\text{ N}$

$F_v=3696\times 10^{-7}\text{ N}$

Comparing this with the given viscous force $3696\times 10^{-x}\text{ N}$, we get:

$x=7$

Answer: $7$