Mechanical Properties of Fluids - Result Question 13
13. The terminal velocity $v_r$ of a small steel ball of radius $r$ falling under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$ depends on mass of the ball $m$, acceleration due to gravity $g$, coefficient of viscosity $\eta$ and radius $r$. Which of the following relations is dimensionally correct?
[1992]
(a) $v_r \propto \frac{m g r}{\eta}$
(b) $v_r \propto m g \eta r$
(c) $v_r \propto \frac{m g}{r \eta}$
(d) $v_r \propto \frac{\eta m g}{r}$
Topic 4: Surface Tension, Surface Energy & Capillarity
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Answer:
Correct Answer: 13. (c)
Solution:
- (c) Note that according to Stoke’s law $6 \pi \eta r v_r=m g$
Hence, the valid relation is $v_r \propto m g / r \eta$
