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A gas bubble from an explosion under water oscillates with a time period $T$ which is proportional to $P ^{a} \rho^{b} E ^{c}$ where $P$ is the pressure, $\rho$ is the density of water and $E$ is the total energy of the explosion. Find the value of $a, b$ and $c$.

The value of a,b and c will be $-\frac{5}{6} ; \frac{1}{2} ; \frac{1}{3}$.
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