terminal velocity hard

Question

Terminal velocity v_t of sphere radius r falling in viscous medium (density difference Δρ) is proportional to:

RankGuru · Accepted Answer

Terminal velocity $v_t$ is reached when the net force on the falling sphere is zero (Viscous Drag + Buoyancy = Gravity).
$6 \pi \eta r v_t = V \rho_{body} g - V \rho_{fluid} g = V \Delta \rho g$
$6 \pi \eta r v_t = \left( \frac{4}{3} \pi r^3 \right) \Delta \rho g$
$v_t = \frac{2 r^2 \Delta \rho g}{9 \eta}$
From this equation, we see that the terminal velocity is proportional to the **square of the radius** ($r^2$).

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terminal velocity hard

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