The terminal velocity v of a small steel ball of radius r falling under gravity through a…
Physics · JEE Main · NTA Exams — Properties of Solids and Liquids
The terminal velocity v of a small steel ball of radius r falling under gravity through a column of viscous liquid of coeffcient of viscosity η depends on mass of the ball m, acceleration due to gravity g, coefficient of viscossity η and radius r. Which of the following relations is dimensionally correct ?
- \(\mathrm{v} \propto \frac{\mathrm{mgr}}{\eta}\)
- \(\mathrm{v} \propto \mathrm{mg} \eta \mathrm{r}\)
- \(\mathrm{v} \propto \frac{\mathrm{mg}}{\mathrm{r} \eta}\)
- \(\mathrm{v} \propto \frac{\eta \mathrm{mg}}{\eta}\)
Answer
(C) v mg r
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