The ratio of radii of two soap bubbles is 2: 1. The ratio of excess pressures inside them is

Question

The ratio of radii of two soap bubbles is 2: 1. The ratio of excess pressures inside them is (A) 1: 2 (B) 1: 4 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

Excess pressure inside the soap bubble is

P = \frac{4 T}{R}

where

T

is the surface tension of the soap solution and

R

is the radius of the bubble.

∴ P_{1} = \frac{4 T}{R _{1}} \dots (i)

and

P_{2} = \frac{4 T}{R _{2}} \dots (ii)

Divide

(i)

by

(ii)

, we get

\frac{P _{1}}{P _{2}} = \frac{R _{2}}{R _{1}} = (\frac{1}{2})

(∵ \frac{R _{1}}{R _{2}} = \frac{2}{1} (Given))

Q. The ratio of radii of two soap bubbles is $2 : 1$ . The ratio of excess pressures inside them is