Question

A solid sphere, of radius R acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity $v_2$, when falling through the same fluid, the ratio $\left(\frac{v_1}{v_2}\right)$ equals:

• A. 27
• B. $\frac{1}{27}$
• C. $\frac{1}{9}$
• D. 9

Answer 1

The correct option is D 9

$v_T\propto R^2$
$R_2={\left[\frac{R^3}{27}\right]}^{\frac{1}{3}}=\frac{R}{3}$
$\frac{v_1}{v_2}=\frac{R^2}{{\left(\frac{R}{3}\right)}^2}=9$