A soap bubble in vacuum has a radius 3, cm an | vedclass

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Question

If $\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}$ be radius of soap bubbles before and after the coalesce and $ \mathrm{p}_{1}, \mathrm{p}_{2}$ and $\ma

Vedclass · Accepted Answer

$5$

Vedclass · Answer

If $\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}$ be radius of soap bubbles before and after the coalesce and $ \mathrm{p}_{1}, \mathrm{p}_{2}$ and $\mathrm{p}$ the pressure then, applying gas laws equation

$\mathrm{p}_{1} \mathrm{V}_{1}+\mathrm{p}_{2} \mathrm{V}_{2}=\mathrm{pV}$

$\frac{4 \mathrm{T}}{\mathrm{r}_{1}} 	imes \frac{4}{3} \pi \mathrm{r}_{1}^{3}+\frac{4 \mathrm{T}}{\mathrm{r}_{2}} 	imes \frac{4}{3} \pi \mathrm{r}_{2}^{3}=\frac{4 \mathrm{T}}{\mathrm{r}} 	imes \frac{4}{3} \pi \mathrm{r}^{3}$

$\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}=\mathrm{r}^{2}$

$3^{2}+4^{2}=r^{2} \Rightarrow r=\sqrt{25}=5 \mathrm{\,cm}$

A soap bubble in vacuum has a radius $3\, cm$ and another soap bubble in vacuum has radius $4\, cm$. If two bubbles coalesce under isothermal condition. Then the radius of the new bubble will be .............. $\mathrm{cm}$

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