Two spheres of radii $r_{1}$ and $r_{2}$ ( $r_{1} > r_{2})$ is dropped through a tube full of glycerine. Their terminal velocities $v_{1}$ and $v_{2}$ are calculated in the experiment. Which of the following is true?

v_{1} = v_{2}

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v_{1} > v_{2}

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v_{1} < v_{2}

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v_{1}

and

v_{2}

are independent of

r_{1}

and

r_{2}

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Solution

The correct option is C $v_{1} > v_{2}$
The expression for the terminal velocity of a perfectly spherical body in a fluid is given by,

$v = \frac{2 (ρ - σ) r^{2} g}{9 η}$

Therefore, for everything else, to be constant, $v \propto r^{2}$

Hence, $v_{1} > v_{2}$

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