A spherical liquid drop of radius acquires the terminal velocity when falls through a gas of viscosity . Now the drop is broken into

Question

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_{1}$ when falls through a gas of viscosity $η$ . Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_{2}$ falling through the same gas. The ratio of terminal velocities $\frac{v_{1}}{v_{2}}$ is ______. [2026]

Smart Achievers · Accepted Answer

(4)

$Using volume conservation,$

$\frac{4}{3} π R_{1}^{3} = 64 \times \frac{4}{3} π R_{2}^{3} \Rightarrow R_{2} = \frac{R_{1}}{4}$

$Terminal velocity v \propto R^{2}$

$\frac{v_{1}}{v_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}} \Rightarrow {(4)}^{2} = 16$

Solution

1 4

2 0.25

3 32

4 16

Ans.
(4)

$Using volume conservation,$

$\frac{4}{3} π R_{1}^{3} = 64 \times \frac{4}{3} π R_{2}^{3} \Rightarrow R_{2} = \frac{R_{1}}{4}$

$Terminal velocity v \propto R^{2}$

$\frac{v_{1}}{v_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}} \Rightarrow {(4)}^{2} = 16$

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