Question

Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1} = 8\pi_{2}\right)$ and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \,\rho_{2}$. The ratio of their terminal velocities would be :

• A. $\frac{79}{72}$
• B. $\frac{19}{36}$
• C. $\frac{39}{72}$
• D. $\frac{79}{36}$

Answer 1

Answer: (D)

$\frac{79}{36}$

Answer 2

$v_r = \frac{2r^2(\sigma - \rho)g}{9\eta}$
$\frac{v_{1}}{v_{2}} = \left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{\left(\sigma_{1} - \rho\right)}{\left(\sigma_{2} - \rho\right)}$
$= \left(\frac{1}{2}\right)^{2} \left(\frac{8\rho_{2} - 0.1 \rho_{2}}{\rho_{2} - 0.1 \rho_{2}}\right) = \frac{79}{36}$