Question

Q. The dimensions of length are expressed as $G^X{C}^Y{h}^Z$, where G,C and h are the universal gravitational constant speed of light and plank's constant respectively. Then

1. X = 1/2, Y = 1/2
2. X= 1/2, Z = 1/2
3. Y = -3/2, Z =1/2
4. Y = 1/2, Z = 3/2

Answer 1

$$\begin{gathered} DearStudent, \\ \left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right] \\ \left[C\right]=\left[L{T}^{-1}\right] \\ \left[h\right]=\left[M^1{L}^2{T}^{-1}\right] \\ \left[L\right]={\left[M^{-1}{L}^3{T}^{-2}\right]}^x{\left[L{T}^{-1}\right]}^y{\left[M^1{L}^2{T}^{-1}\right]}^z \\ -x+z=0........1 \\ 3x+y+2z=1.........2 \\ -2x-y-z=0........3 \\ add2and3 \\ x+z=1 \\ z-x=0 \\ 2z=1 \\ z=\frac{1}{2} \\ x=\frac{1}{2} \\ y=\frac{-3}{2} \\ Regards \end{gathered}$$