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

The energy (E), angular momentum (L) and universal gravitational const

1.	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
Answer» zero `-1` `5//3` `1` Solution :(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`