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Relative Velocity in 2D

A bomb explod...

Question

A bomb explodes at time $t = 0$ in a uniform, isotropic medium of density $ρ$ and releases energy E, generating a spherical blast wave. The radius R of this blast wave varies with time t as.

A

t

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B

t^{2 / 5}

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C

t^{1 / 4}

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D

t^{3 / 2}

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Solution

The correct option is A $t^{2 / 5}$
The blast energy E, radius R, density $ρ$ and time t are related by
$\frac{E t^{2}}{ρ R^{5}} = c o n s t a n t$
Hence, R is $\propto t^{\frac{2}{5}}$

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