Question

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble what is the ratio between the volume of the first and second level

Answer 1

ihope it correct sir

Answer 2

The ratio of volume of the first bubble and the second bubble is $\frac{1}{27}$.

Explanation:

The pressure inside the soap bubble,

                                        ⇒ $P_{1}$ = $\frac{4T}{r}$

where, T is the surface tension and r is the radius of the bubble.

The pressure inside the second soap bubble,

                                          ⇒ $P_{2}$ = $\frac{4T}{R}$

where, R is the radius of the second bubble.

Now, ratio of volumes,

⇒ $\frac{V_{1} }{V_{2} } = \frac{\frac{4\pi r^{3}}{3} }{\frac{4\pi R^{3} }{3} }$

   ⇒ $\frac{r }{R} = \frac{1}{27}$

Hence, the ratio of the volumes are

   ⇒  $\frac{V_{1} }{V_{2} } = \frac{1}{27}$