Physics - Unit & Dimension Question with Solution | TestHub

Given:

$m\mathit{=}k{c}^P{G}^{-1/2}\mathit{ }{h}^{1/2}$

Writing dimensions on both sides, we get

$\left[{\mathrm{M}}^1 {\mathrm{L}}^0 {\mathrm{T}}^0\right]={\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{P}}{\left[{\mathrm{M}}^{-1} {\mathrm{L}}^3 {\mathrm{T}}^{-2}\right]}^{-1/2}{\left[{\mathrm{ML}}^2 {\mathrm{T}}^{-1}\right]}^{1/2}$

By comparing exponent of $\mathrm{L}$ on both the sides, we get

$$\begin{gathered} 0=P-\frac{3}{2}+1 \\ \Rightarrow P=\frac{1}{2} \end{gathered}$$