Test Academy | A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity. After some time the velocity of the ball attains a constant value known as terminal velocity vₜ. The terminal velocity depends on (i) the mass of the ball. (ii) η (iii) r and (iv) acceleration due to gravity g. which of the following relations is dimensionally correct vₜ ∝ mg/ηr, vₜ ∝ ηr/mg, vₜ ∝ ηrmg, vₜ ∝ mgr/η

Question

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity. After some time the velocity of the ball attains a constant value known as terminal velocity vₜ. The terminal velocity depends on (i) the mass of the ball. (ii) η (iii) r and (iv) acceleration due to gravity g. which of the following relations is dimensionally correct

Options :

vₜ ∝ mg/ηr
vₜ ∝ ηr/mg
vₜ ∝ ηrmg
vₜ ∝ mgr/η

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