In an environment with a density of $\rho_0$, a point explosion with an energy of $E_0$ occurred, which caused an expanding shock wave with a radius of $R$. In the first approximation, the dependence $R(t)$ will be power-law for each of the arguments $\rho_0, E_0, t$:

\[R = S(\gamma) \cdot E^a_0 \cdot \rho_0^b \cdot t^c,\]where $S(\gamma)$ is a dimensionless constant depending on the gas.

А1 Analyzing the dimensions, find $a$, $b$ and $c$.

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A2 Above are photos of the first atomic explosion, taken milliseconds after detonation. At each photo the scale and time from the beginning of the explosion are indicated. Having linearized the dependence from point A1, find the energy $E_0$ that the atomic bomb released. The air density is $1.3~\text{kg}/\text{m}^3$. The coefficient $S$ for air is $S = 1.03$.

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