A water drop of radius $1\,\mu m$ falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is $1.8 \times 10^{-5}\,Nsm ^{-2}$ and its density is negligible as compared to that of water $10^{6}\,gm ^{-3}$. Terminal velocity of the water drop is________ $\times 10^{-6}\,ms ^{-1}$
(Take acceleration due to gravity $=10\,ms ^{-2}$ )
JEE MAIN 2022, Medium
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$6 \pi \eta r v _{ t }=\frac{4}{3} \pi r ^{3} \rho g$
$v _{ t }=\frac{4}{3} \times \frac{\pi r^{3} \rho g }{6 \pi \eta r}$
$v _{ t }=\frac{4}{3} \times \frac{\pi r ^{3} \rho g }{6 \pi \eta r}=\frac{2 \times 10^{-12} \times 10^{3} \times 10}{9 \times 1.8 \times 10^{-5}}$
$=123.4 \times 10^{-6}\,m / s$
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