The terminal velocity of a sphere of radius $r$, density $\rho$ falling through a fluid of viscosity $\eta$ and density $\sigma$ is:
A$v_t = (2/9) r^2 (\rho - \sigma) g / \eta$
B$v_t = (2/9) r^2 (\rho + \sigma) g / \eta$
C$v_t = 6\pi \eta r g$
D$v_t = 6\pi r^2 g / \eta$
Answer & Solution
Correct answer: A. $v_t = (2/9) r^2 (\rho - \sigma) g / \eta$
At terminal velocity: $\frac{4}{3}\pi r^3 \rho g = 6\pi\eta r v_t + \frac{4}{3}\pi r^3 \sigma g$. Solving: $v_t = (2 r^2 g (\rho - \sigma))/(9\eta)$.
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