A rain drop of radius 1.5 mm, experiences a drag force $F = (2 \times 10^{- 5} V) N$ , while falling through air from a height 2km, with a velocity v. The terminal velocity of the rain drop will be nearly (use g = 10m/s^2-)

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200 m/s

80 m/s

3 m/s

4.7 m/s

answer is C.

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Detailed Solution

$\begin{array}{l} F = mg \\ F = 2 \times 10^{- 5} v = \frac{4}{3} π {(1 .5 \times 10^{- 3})}^{3} \times 10^{3} \times 10 \\ \Rightarrow v = \frac{2 π}{3} \times (2 .25) = 4 .7 m / s \end{array}$

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