Question

Pressure inside two soap bubble are 1.01 and 1.03 aim, ratio between their volume is

• A. 27:1
• B. 3:1
• C. 127:101
• D. None of these

Answer 1

Answer: (A)

Excess pressure as compared to atmosphere inside bubble A is $\Delta p_1=1.01-1$ $=0.01\text{atm}$ Inside bubble B is $\Delta p_2=1.03-1$ $=0.03\text{atm}$ $\rho =\frac{4T}{r}$ Let $r_1$ and $r_2$ be the radii of bubbles A and 8 respectively, then $\frac{p_1}{p_2}=\frac{4T/r_1}{4T/r_2}$ $=\frac{0.01}{0.03}$ $\frac{r_2}{r_1}=\frac{1}{3}$ Since, bubbles are spherical in shape, their volumes are in the ratio $\frac{V_1}{V_2}=\frac{4/3\pi r_1^3}{4/3\pi r_2^3}$ $\frac{V_1}{V_2}={\left(\frac{3}{1}\right)}^3$ $=\frac{27}{1}$ $v_1:v_2=27:1$