a
Let time, \(T \propto c^{x} G^{y} h^{z}\)

\(\Rightarrow T=k c^{x} G^{y} h^{z}\)

Taking dimensions on both sides \(\left[M^{0} L^{0} T^{1}\right]=\left[L T^{-1}\right]^{x}\left[M^{-1} L^{3} T^{-2}\right]^{y}\left[M L^{2} T^{-1}\right]^{z}\)

\(i . e\)

\(\left[M^{0} L^{0} T^{1}\right]=\left[M^{-y+z} L^{x+3 y+2 z} T^{-x-2 y-z}\right]\)

Equating power of \(M, L,\) Ton both sides, we get

\(-y+z=0 \quad \ldots(1)\)

\(x+3 y+2 z=0 \quad \ldots(2)\)

\(-x-2 y-z=1 \quad \ldots .(3)\)

From \((1) \Rightarrow z=y\)

Adding (2) and \((3) \Rightarrow y+z=1\)

or \(2 y=1 \quad[\text { From }]\)

i.e, \(y=\frac{1}{2}\)

\(\therefore z=y=\frac{1}{2}\)

Putting these values in (2) we get \(x+\frac{3}{2}+1=0\) or \(x=\frac{-5}{2}\)

Hence\(,[T]=\left[G^{1 / 2} h^{1 / 2} c^{-5 / 2}\right]\)