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Two uniform solid balls of same density and of radii r and 2r are dropped in air and fall vertically downwards. The terminal velocity of the ball with radius r is 1 $cm s^{- 1}$ , then the terminal velocity of the ball of radius 2r will be (neglect buoyant force on the balls.)

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0.5 $cm s^{- 1}$

4 $cm s^{- 1}$

1 $cm s^{- 1}$

2 $cm s^{- 1}$

answer is B.

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Detailed Solution

At equilibrium

$mg = 6 {πηrv}_{0} or ρ \frac{4 π}{3} r^{3} g = 6 πηrv$

$∴ \frac{v_{r}}{v_{2 r}} = \frac{{(r)}^{2}}{{(2 r)}^{2}} or v_{2 r} = (v_{r}) \times 4 = 4 cm / s$

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