Question 124 of 192

A spherical soap bubble of radius $3cm$ is formed inside another spherical soap bubble of radius $6cm$. If the internal pressure of the smaller bubble of radius $3cm$ in the above system is equal to the internal pressure of the another single soap bubble of radius $rcm$. The value of $r$ is _____

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Answer: 2

Pressure inside a bubble is given by, ${P}_{0}+\dfrac{4T}{r}$.
Pressure inside the bubble of smaller radius will be,
${P}_{2}-{P}_{1}=\left[\left({P}_{0}+\dfrac{4T}{6}\right)+\dfrac{4T}{3}\right]$
Pressure inside the bubble with radius $r$, ${P}_{0}+\dfrac{4T}{r}$
Now,
$\Rightarrow {P}_{0}+\dfrac{4T}{6}+\dfrac{4T}{3}={P}_{0}+\dfrac{4T}{r}$
$\Rightarrow \dfrac{1}{r}=\dfrac{1}{6}+\dfrac{1}{3}$
$\Rightarrow r=2cm$