If mass is written as m = k c ^ P G ^ - 1 / 2 h ^ 1 / 2 , then the...

Given:

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

Writing dimensions on both sides, we get

\left[{M}^{1}{L}^{0}{T}^{0}\right] = {\left[{LT}^{- 1}\right]}^{P}{\left[{M}^{- 1}{L}^{3}{T}^{- 2}\right]}^{- 1 / 2}{\left[{ML}^{2}{T}^{- 1}\right]}^{1 / 2}$</p><p>By comparing exponent of$L$on both the sides, we get</p><p>$0 = P - \dfrac{3}{2} + 1 ⇒ P = \dfrac{1}{2}