Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through the air of viscosity 1.8 x 10-5 N/m2 will be
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a
10.9 m/s
b
8.3 m/s
c
9.2 m/s
d
7.6 m/s
answer is A.
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Detailed Solution
The terminal velocity of the spherical raindrop of radius r is given byvt=2r2ρ-σg9ηwhere ρ is the density of water and σ the density of air and η is viscosity of air. Substituting r=0.3mm=0.3×10-3m, ρ=103kg/m3g=9.8ms−2 and η=1.8×10−5Ns/m2Compared to water, we can neglect density of air. We get vt=2×(0.3×10-3)2×103×9.89×1.8×10−5=10.9m/s