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

Putting the dimensions in the above relation

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

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

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)

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

Hence dimension of time are \(\left[ G^{1/2} A^{1/2} C^{-5/2} \right]\)