Question

A gas bubble, from an explosion under water, oscillates with a period $T$ proportional to $P^a{d}^b{E}^c$, where $P$ is the static pressure, $d$ is the density of water and $E$ is the total energy of the explosion. The values of $a$.......... $b$........... and $c$............ .

Answer 1

$T\alpha P^a{d}^b{E}^c$

$\Rightarrow T=\left(M{L}^{-1}{T}^{-2}{)}^a\right(M{L}^{-3}{)}^b(M{L}^2{T}^{-2}{)}^c$

$\Rightarrow a+b+c=0,-a-3b+2c=0,-2a-2c=1$

$\Rightarrow a=\frac{-5}{6},b=\frac{1}{2},c=\frac{1}{3}$