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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None of these

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Solution

The correct option is D
None of these

$v = K r_{1}^{2}$
$4 v = K r_{2}^{2}$
$\Rightarrow r_{2}^{2} = 4 r_{1}^{2}$
$\Rightarrow r_{2} = 2 r_{1}$
Since n drops of radius $r_{1}$ make a drop of radius $r_{2}$
$\frac{4}{3} π r_{2}^{3} = n \frac{4}{3} π r_{1}^{3}$
$\Rightarrow r_{2}^{3} = n r_{1}^{3}$
$\Rightarrow (2 r_{1})^{3} = n r_{1}^{3}$
n=8

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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.

The correct option is D None of these v=Kr21 4v=Kr22 ⇒r22=4r21 ⇒r2=2r1 Since n drops of radius r1 make a drop of radius r2 43πr32=n43πr31 ⇒r32=nr31 ⇒(2r1)3=nr31 n=8