Time \(y c^{y} G^{/} h^{2} \to T = k c^{*} G^{:} h^{'}\)

Putting the dimensions in the above relation

\(\Rightarrow\) \(\left[M^{2} L^{3} T^{-1}\right]=\left[L T^{-1}\right]^{x}\left[M^{-1} L^{2} T^{-2}\right]^{y}\left[M L^{2} T^{-1}\right]^{z}\)

\(\Rightarrow\) \(\left[ M^{D} L^{D} T^{1} \right] = \left[ M^{1} \cdot L^{2} \cdot L^{-3} \cdot T^{-1} \cdot A^{-1} \cdot L^{2} \right]\)

Comparing the powers of M, L and \tau

- y - 7 = 0 …(i)

x + 3y + 2z = 0 … (ii)

-x - 2y - 7 = 1 … (iii)

On solving equations (i) and (ii) and (iii)

\(x = -\frac{5}{2}, y = z - \frac{1}{2}\)

Hence dimension of time are \(\left[ G^{1.2} A^{1.2} C^{-5.2} \right]\)