Fluid Mechanics

JEE Main level, single correct, medium

186 of 192

Question 186 of 192

A raindrop with radius R=0.2mmR=0.2mm falls from a cloud at a height h=2000mh=2000m 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=1000kgm−3{f}_{w}=1000kg{m}^{-3} and Density of air fa=1.2kgm−3,g=10m/s2{f}_{a}=1.2kg{m}^{-3},g=10m/{s}^{2} Coefficient of viscosity of air =1.8×10−5Nsm−2]\left.=1.8\times {10}^{-5}Ns{m}^{-2}\right]

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Answer: (C) 4.94ms−14.94{ms}^{-1}

At terminal speed
a=0a=0
Fnet=0{F}_{net}=0
mg=Fv=6πηRvmg={F}_{v}=6\pi \eta Rv
V=mg6πηRVV=\dfrac{mg}{6\pi \eta RV}
v=ρw4π3R3g6πηRv=\dfrac{{\rho }_{w}\dfrac{4\pi }{3}{R}^{3}g}{6\pi \eta R}
=2ρwR2g9η=\dfrac{2{\rho }_{w}{R}^{2}g}{9\eta }
=40081m/s=\dfrac{400}{81}m/s
=4.94m/s=4.94m/s

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