Physics - Unit & Dimension Question with Solution | TestHub

$\because [\mathrm{V}]=[\mathrm{b}]$ $\therefore$ Dimension of $b=\left[{\mathrm{L}}^3\right]$ $\begin{array}{rl}& \&[\mathrm{P}]=\left[\frac{\mathrm{a}}{{\mathrm{V}}^2}\right]\\ & [\mathrm{a}]=\left[{\mathrm{PV}}^2\right]=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]\left[{\mathrm{L}}^6\right]\end{array}$ Dimension of $\mathrm{a}=\left[{\mathrm{ML}}^5{\mathrm{T}}^{-2}\right]$ $\therefore {\mathrm{ab}}^{-1}=\frac{\left[{\mathrm{ML}}^5{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{L}}^3\right]}=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$