Radially oscillating charged soap bubble

A neutral soap bubble has a radius RR, mass MM, and the liquid making its boundary has surface tension σ\sigma. Now, this soap bubble is given a very small charge qq. Afterwards , it begins oscillating radially(i.e. its radius oscillates with a particular frequency).The time period of these oscillations can be shown as T0=aπMbPAR+cσT_{0} = \sqrt{\dfrac{a \pi M}{b P_{A} R + c \sigma}}, where PAP_{A} is atmospheric pressure, and a,b,ca,b,c are co-prime integers . Find the value of a+b+ca+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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