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A solid sphere of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity v2 when falling through the same fluid, the ratio (v1/v2) equals:
- 1/9
- 1/27
- 9
- 27
Correct answer: 9
Solution
Terminal velocity v ~ R^2. Breaking into 27 equal spheres gives each radius R/3, so v2 = v1*(1/3)^2 = v1/9. Hence v1/v2 = 9.
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