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Question

If n identical water droplets falling under gravity with terminal velocity v coalesce to form a single drop which has the terminal velocity 4v, find the number n.

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Solution

No of identical water dropletts falling falling under gravity=n
Thermal velocity=V
And then coalesce to form a single drop
The thermal velocity ==4V
Find n
The terminal velocity of an object is directly proportional to the square of the radius of the drop. The volume of the small drop is 43πr3. The volume of the bigger drop formed by collection of N drops is N43πR3
(R be the radius of the bigger droplet and r be the radius of the smaller droplet)
Thus the radius of the bigger drop is R=N1/3×r(V2V1)=(Rr)2)(V2V1)=(rN1/3r)2×V2V1=N2/34V=N2/3VN=8

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