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

Step-by-step solution

aligned & h G^x L^y E^z & [ M ^1 ~L ^2 ~T ⁻¹ ] [ M ⁻¹ ~L ^3 ~T ⁻² ]^x [ M ^1 ~L ^2 ~T ⁻¹ ]^y [ M ^1 ~L ^2 ~T ⁻² ]^z & [ M ^1 ~L ^2 ~T ⁻¹ ]=k [ M ⁻¹ ~L ^3 ~T ⁻² ]^x [ M ^1 ~L ^2 ~T ⁻¹ ]^y aligned [ M ^1 ~L ^2 ~T ⁻² ]^z Comparing the powers, we get aligned 1 & =-x+y+z 2 & =3 x+2 y+2 z -1 & =-2 x-y-2 z aligned On solving Eq. (i), (ii) and (iii), we get x=0