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The terminal velocity v  of small steel ball of radius r  falling under gravity through a column of viscous liquid of coefficient of viscosity η  depends on mass of the ball m, acceleration due to gravity g, coefficient of viscosity η  and radius  r. which of the following relations is dimensionally correct?

Option: 1

v \propto \frac{m g r}{\eta}


Option: 2

v \propto mg\eta\,r


Option: 3

v \propto \frac{m g }{r\eta}


Option: 4

v \propto {\eta}


Answers (1)

best_answer

\text { Use, } F=6 \pi \eta r v, \text { v has the dimensions }

\text { of } \frac{F}{\eta r} \text { or } \frac{m g}{\eta r}

v \propto \frac{m g }{r\eta}

Posted by

Suraj Bhandari

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