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Eight identical droplets of water were falling in air with constant velocity $2 c m / s .$ The initial acceleration of each droplet was $' a_{1}'$ at the time when they start falling. At a time $' t',$ these droplets coalesce to form a big drop due to pressure difference developed and just after the formation of combined drop, its acceleration is found $' a_{2}' .$ The ratio of $\frac{3 a_{1}}{a_{2}}$ is

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answer is 4.

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Detailed Solution

$m_{1} a_{1} = 6 π η r_{1} v_{1}$

$m_{2} a_{2} = 6 π η r_{2} (v_{2} - v_{1})$

$\frac{a_{1}}{a_{2}} = \frac{r_{1} v_{1} m_{2}}{r_{2} (v_{2} - v_{1}) m_{1}} = \frac{4}{3}$

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