# Radially oscillating charged soap bubble

A neutral soap bubble has a radius $R$, mass $M$, and the liquid making its boundary has surface tension $\sigma$. Now, this soap bubble is given a very small charge $q$. Afterwards , it begins oscillating radially(i.e. its radius oscillates with a particular frequency).The time period of these oscillations can be shown as $T_{0} = \sqrt{\dfrac{a \pi M}{b P_{A} R + c \sigma}}$, where $P_{A}$ is atmospheric pressure, and $a,b,c$ are co-prime integers . Find the value of $a+b+c$.

Details and assumptions

$\bullet$ The gas inside the bubble is ideal and mono-atomic.

$\bullet$ No heat exchange takes place, i.e. the boundary is insulating.

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