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.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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

Suggest Corrections

Similar questions

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.

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

4

v, find the number n.

Two liquid drops of same radius are falling through air with a terminal velocity ‘v’. If the drops coalesce to form a single drop, the terminal velocity will be

Q. Two identical drops falling with a terminal speed 'v' coalesce to form a bigger drop. The terminal velocity of the bigger drop will be

Q. Twenty-seven rain drops of same diameter fall through air with terminal velocity '

V

'. If they coalesce forming a single drop, then the terminal velocity of the resultant drop is

Join BYJU'S Learning Program

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