Physics - Unit & Dimension Question with Solution | TestHub

$\left[{\mathrm{MLT}}^{-2}\right]=\left[{\mathrm{L}}^{2\mathrm{a}}\right]\times \left[{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{-\mathrm{b}}\right]\left[{\mathrm{M}}^{\mathrm{c}}{\mathrm{L}}^{-3\mathrm{c}}\right]$ $$=\left[{\mathrm{M}}^{\mathrm{c}}{\mathrm{L}}^{2\mathrm{a}+\mathrm{b}-3\mathrm{c}}{\mathrm{T}}^{-\mathrm{b}}\right]$$ Comparing powers of $\mathrm{M},\mathrm{L}$ and $\mathrm{T},$ on both sides, we get $$\begin{array}{l}\mathrm{c}=1,2\mathrm{a}+\mathrm{b}-3\mathrm{c}=1,-\mathrm{b}=-2\text{ or }\mathrm{b}=2\\ \text{ Also, }2\mathrm{a}+2-3(1)=1\Rightarrow 2\mathrm{a}=2\text{ or }\mathrm{a}=1\end{array}$$ $\therefore$ This is 1,2,1