Two metal balls of densities ‘d’ and ‘3d’ and radii $r_{1}$ and ‘ $r_{2}$ ’ are travelling in the same liquid. The density of the liquid is ‘d/2’. The ratio of their terminal velocities is 4:5 respectively. Then the ratio of their radii is

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5:12

4:5

2:1

3:4

answer is C.

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Detailed Solution

terminal velocity $v_{} = \frac{2 r^{2} (d_{s} - d_{l}) g}{9 η}$

$\frac{v_{1}}{v_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} \frac{(d - \frac{d}{2})}{(3 d - \frac{d}{2})} = \frac{4}{5}$

$\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{4}{5} \frac{5}{1} = 4$ $\Rightarrow \frac{r_{1}}{r_{2}} = 2$

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