Question

An air bubble just inside a soap solution and a soap bubble blown using the same solution have their radii in the ratio 3 : 2. The ratio of the excess pressure inside them is 

(A) 1 : 12 

(B) 1 : 6 

(C) 1 : 3 

(D) 1 : 2.

Answer 1

Correct Option is (C) 1 : 3

Given,

\(R_1 = 3\)

\(R_2 = 2\)

Pressure \(\Delta P_1 = \frac{4 S}{r_1}\)

Inside \(\Delta P_2 = \frac{8S}{R_2}\)

\(\frac{\Delta P_1}{\Delta P_2} = \frac{4S}{R_1} \times \frac{R_2}{8S}\)

\(= \frac{R_2}{2R_1}\)

\(\frac{\Delta P_1}{\Delta P_2} = \frac{2}{2 \times 3}\)

\(\frac{\Delta P_1}{\Delta P_2} = \frac{1}{3}\)

\(\Delta P_1 : \Delta P_2 = 1 : 3\)

Answer 2

Correct option is (C) 1 : 3