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(iii) 27 number of droplets having same ...

(iii) 27 number of droplets having same size are falling through air with the same terminal velocity of `1m. S^-1`. If the small droplets merge to produce a new drop, what will be the terminal velocity of the new drop?

Text Solution

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The terminal velocity of a moving droplets is proportional to the square of its radius.
When 27 number of droplets having same size merge and form a new drop then the volume of the new drop becomes 27 times the volume of each small drop.
Hence, the radius of the new drop becomes `root(3)(27)` times or 3 times.
So, the terminal velocity will be `(3)^2` or 9 times,
`therefore` The terminal velocity of the new drop
`=9xx1=9m. s^-1`
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