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JEE Main 202127 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2021 · 27 July · Evening Shift · Physics · Mechanical Properties of Fluids

A raindrop with radius R = 0 . 2mm falls from a cloud at a height h...

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−3andDensityofair{f}_{w} = 1000kg{m}^{- 3} and Density of air{f}_{a} = 1 . 2kg{m}^{- 3}, g = 10m / {s}^{2}Coefficient of viscosity of air \left= 1 . 8 \times {10}^{- 5}Ns{m}^{- 2}\right]

Options

  1. A250.6ms−1250 . 6{ms}^{- 1}
  2. B43.56ms−143 . 56{ms}^{- 1}
  3. C4.94ms−14 . 94{ms}^{- 1}
  4. D14.4ms−114 . 4{ms}^{- 1}

Correct answer

C. 4.94ms−14 . 94{ms}^{- 1}

Step-by-step solution

At terminal speed

a=0a = 0

Fnet=0{F}_{net} = 0

mg=Fv=6πηRvmg = {F}_{v} = 6\piηRv

V=mg6πηRVV = \dfrac{mg}{6\piηRV}

v=ρw4π3R3g6πηRv = \dfrac{{ρ}_{w}\dfrac{4\pi}{3}{R}^{3}g}{6\piηR}

=2ρwR2g9η= \dfrac{2{ρ}_{w}{R}^{2}g}{9η}

=40081m/s= \dfrac{400}{81}m / s

=4.94m/s= 4 . 94m / s

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