The excess of pressure inside a soap bubble is twice the excess of pressure inside another soap bubble. The volume of first bubble is ‘n’ times the volume of second bubble. The value of ‘ $n$ ‘ must be
A. $0.125$
B. $0.25$
C. $2$
D. $0.5$
The excess of pressure inside a soap bubble is twice the excess of pressure inside another soap bubble. The volume of first bubble is ‘n’ times the volume of second bubble. The value of ‘ $n$ ‘ must be
A. $0.125$
B. $0.25$
C. $2$
D. $0.5$

Correct answer is A.

Given,
$\frac{4 \mathrm{~T}}{\mathrm{r}_{1}}=2 \times \frac{4 \mathrm{~T}}{\mathrm{r}_{2}}$ or $\mathrm{r}_{2}=2 \mathrm{r}_{1}$
$\frac{4}{3} \pi \mathrm{r}_{1}^{3}=\mathrm{n} \times \frac{4}{3} \pi \mathrm{r}_{2}^{3}=\mathrm{n} \times \frac{4}{3} \pi\left(2 \mathrm{r}_{1}\right)^{3}$ or $\mathrm{n}=\frac{1}{8}=0.125$