GATE Mechanical 2023 | Question: 55

Question

An explosion at time $t=0$ releases energy $\text{E}$ at the origin in a space filled with a gas of density $\rho$. Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure.

Let $\text{R}$ denote the radius of the front of the hemispherical blast wave. The radius $\text{R}$ follows the relationship $R=k t^a E^b \rho^c$, where $k$ is a dimensionless constant. The value of exponent $\text{a}$ is _____________.

(Rounded off to one decimal place)