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Two drops of equal radii are falling through air with a termin

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Two drops of equal radii are falling through air with a terminal velocity of $5 c m s^{- 1}$ . If they coalesce into one drop, what will be the terminal velocity of the new drop?

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Two drops of equal radii are falling through air with a terminal velocity of

5 c m s^{- 1}

. If they coalesce into one drop, what will be the terminal velocity of the new drop?

15 mins ago

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15 mins ago

Text solutionVerified

Let

x

be the radius of each drop

The terminal velocity

(v) = \frac{2}{9} . r^{2} \frac{( ρ 5 ) g}{4}

where

5

and

4

are the density and vescosity at are respectively

ρ

is the density of the drop

Volume at each drop

= \frac{4}{3} \times r^{3}

The volume of coalesed drop

= 2 \times \frac{4}{3} \times r^{2} = \frac{4}{3} \times (2^{1/3} r)^{3}

So Radius of collapsed drop

= (2)^{1/3} r

∴

Now the terminal velocity at the collapsed drop

v = 4 (2^{1/3} r)^{2} = 2^{2/3} 4 r^{2} = 2^{2/3} v

∴

Hence the terminal velocity of the collapsed drop is

7.94 c m / s

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Question Text	Two drops of equal radii are falling through air with a terminal velocity of $5 c m s^{- 1}$ . If they coalesce into one drop, what will be the terminal velocity of the new drop?
Answer Type	Text solution:1
Upvotes	150