Question

Two solid spherical balls of radius r₁& r₂(r₂< r₁), of density s are tied up with a string and released in a viscous liquid of lesser density r and coefficient of viscosity h, with the string just taut as shown. The terminal velocity of spheres is-

• A. $\frac{2}{9}\frac{r_{2}^{2}g}{\eta}(\sigma - \rho)$
• B. $\frac{2}{9}\frac{r_{1}^{2}g}{\eta}(\sigma - \rho)$
• C. $\frac{2}{9}\frac{(r_{1}^{3} + r_{2}^{3})}{r_{1} + r_{2}}\frac{(\sigma - \rho)g}{\eta}$
• D. $\frac{2}{9}\frac{(r_{1}^{3} - r_{2}^{3})}{r_{1} - r_{2}}\frac{(\sigma - \rho)g}{\eta}$

Answer 1

Answer: (C)

$\frac{2}{9}\frac{(r_{1}^{3} + r_{2}^{3})}{r_{1} + r_{2}}\frac{(\sigma - \rho)g}{\eta}$

Answer 2

at terminal velocity net force is zero.

6ph(r₁ + r₂) V_T+$\frac{4}{3}$p (r₁³+r₂³)rg=$\frac{4}{3}$p (r₁³ + r₂³) sg