The potential damage to an object $($e$.$g$.$ a tank, house, etc$)$ due to an explosion or blast wave is related to the pressure difference $($AP$)$ experienced by the object. The pressure difference is a function of the distance $($r$)$ from the blast centre, time $($t$),$ speed of sound in the medium $($c$),$ and total energy $($E$)$ in the blast. $($Total: $16$ marks$)$ Use dimensional analysis to describe the relationships among these variables using r$,$ E and t as repeating variables. $(8$ marks$)$ Consider an object subjected to a blast in air $($speed of sound $350$ m$/$s$)$ in the following two different cases: Case $1$: object is $3$ in away, time $2$ sec$,$ blast energy is $5$ MJ$.$ Case $2$: object is $6$m away, time is $4$ seconds, blast energy is $10$ MJ$.$ What you predict the ratio of the pressure difference in case $1$ to case $2$