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  4. A raindrop with radius R=0.2 mm falls from a cloud at a height h=2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is: [Density of water fw=1000 k gm -3 and Density of air fa=1.2 kgm -3, g=10 m / s 2 Coefficient of viscosity of air =1.8 × 10-5 Nsm -2 ]

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Q. A raindrop with radius $R=0.2\, mm$ falls from a cloud at a height $h=2000\, m$ above the ground.
Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water $f_{w}=1000\, k\, gm ^{-3}$ and Density of air $f_{a}=1.2\, kgm ^{-3}, g=10\, m / s ^{2}$ Coefficient of viscosity of air $=1.8 \times 10^{-5}\, Nsm ^{-2}$ ]

JEE MainJEE Main 2021Mechanical Properties of Fluids

Solution:

At terminal speed
$a=0$
$F_{\text{net}}=0 $
$m g=F_{v}=6 \pi \eta R v$
$v=\frac{m g}{6 \pi \eta R v} $
$v=\frac{\rho_{w} \frac{4 \pi}{3} R^{3} g}{6 \pi \eta R}$
$=\frac{2 \rho_{w} R^{2} g}{9 \eta}=\frac{400}{81} m / s $
$=4.94\, m / s$