Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :
Question:

Pressure inside two soap bubbles are $1.01$ and $1.02$ atmosphere, respectively. The ratio of their volumes is :

1. (1) $4: 1$

2. (2) $0.8: 1$

3. (3) $8: 1$

4. (4) $2: 1$

Correct Option: , 3

Solution:

(3) According to question, pressure inside, 1st soap bubble,

$\Delta P_{1}=P_{1}-P_{0}=0.01=\frac{4 T}{R_{1}}$             ….(1)

And $\Delta P_{2}=P_{2}-P_{0}=0.02=\frac{4 T}{R_{2}}$        ….(2)

Dividing, equation (ii) by (i),

$\frac{1}{2}=\frac{R_{2}}{R_{1}} \Rightarrow R_{1}=2 R_{2}$

Volume $V=\frac{4}{3} \pi R^{3}$

$\therefore \frac{V_{1}}{V_{2}}=\frac{R_{1}^{3}}{R_{2}^{3}}=\frac{8 R_{2}^{3}}{R_{2}^{3}}=\frac{8}{1}$