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Two spherical balls of radius \( r_{1} \) and \( r_{2}\left(r_{1}\right) \) and of density \( \sigma \) are tied up with a long string and released in a viscous liquid column of lesser density \( \rho \) with the string just taut as shown. Find the tension in the string when terminal velocity is attained :
(a) \( \frac{3}{4} \pi\left(\frac{r_{2}^{4}-r_{1}^{4}}{r_{2}-r_{1}}\right)(\sigma-\rho) g \)
(b) \( \frac{2}{3} \pi\left(r_{2}^{4}-r_{1}^{4}\right)(\sigma-\rho) g \)
(c) \( \frac{4}{3} \pi\left(r_{2}^{4}-r_{1}^{3}\right)(\sigma-\rho) g \)
(d) \( \frac{4}{3} \pi r_{1} r_{2}\left[r_{1}-r_{2}\right](\sigma-\rho) g \)
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