The energy `(E)`, angular momentum `(L)` and universal gravitational constant `(G)` are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant `h` is

Options

A. zero
B. `-1`
C. `5//3`
D. `1`

Explanation

(a) `hprop G^(x)L^(y)E^(z)`
Write the dimensions on both sides
`[ML^(2)T^(-1)]prop[M^(-1)L^(3)T^(-2)]^(x)[ML^(2)T^(-1)]^(y)[ML^(2)T^(-2)]^(z)`
`[ML^(2)T^(-1)]=k[M^(-1)L^(3)T^(-2)]^(x)[ML^(2)T^(-1)]^(y)[ML^(2)T^(-2)]^(z)`
Comparing the powers, we get
`1=-x+y+z`...........(i)
`2=3x+2y+2z` .........(ii)
`-1=-2x=y-2z`...........(iii)
On solving eqs (i), (ii) and (iii) we ger
`x=0`