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The terminal velocity vr of a small steel ball of radius r falling under gravity through a column of a 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 ?
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vr ∝ mgr η - vr ∝ mg η r
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vr ∝ mg rη -
vr ∝ η mg r
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Correct Option: C
Note that according to Stoke's law
6π η rvr = mg
Hence, the valid relation is vr ∝ mg / rη