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 buoyancy may be neglected, then the terminal speed attained by the raindrop is:

[Density of water fw=1000 kgm-3 and Density of air fa=1.2 kgm-3, g=10m/s2. Coefficient of viscosity of air=1.8×10-5Nsm-2]

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a

43.56 ms-1

b

14.4  ms-1

c

250.6  ms-1

d

4.94  ms-1

answer is B.

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Detailed Solution

Given,

Radius r =0.2mm, height h =2000m

The velocity will be constant when the plummet reaches its terminal speed (v), hence a=0.

Fnet=0

Question Image

mg=Fv=6πηRv  

v=mg6πηR =ρw(43πR3)g6πηR =2ρwR2g9η 

v=2×1000×(0.2×10-3)2×109×1.8×10-5 =4.94 m/s

Hence the correct answer is 4.94m/s.

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