If the energy, `E = G^p h^q c^r,` where G is the universal gravitational constant, h is the Planck's constant and c is the velocity of light, then the values of p are q and r are, respectively

Options

A. `-1//2, 1//2` and `5//2`
B. `1//2, -1//2` and `-5//2`
C. `-1//2, 1//2` and `3//2`
D. `1//2, 1//2` and `-3//2`

Explanation

`E=G^(p)h^(q)C^(r)`
Dimensionally
`[M^(1)L^(2)T^(-2)]=[M^(-1)L^(3)T^(-2)]^(p)[M^(1)L^(2)T^(-1)]^(q)[LT^(-1)]^(c)`
`[M^(1)L^(2)T^(-2)]=[M^(-p)L^(3p)T^(-2p)][M^(q)L^(2q)L^(2qT)][L^(c)T^(-c)]`
`[M^(1)L^(2)T^(-2)[M^(-p+q)L^(3p+2q+c)T^(-2p-q-c)]`
`rArr-p+q=1`
`rArr2p+2q+c=2`
`rArr-2p-q+c=-2`
`s 0 1 v i (1)/(2),qg=(1)/(2),r=w(5)/(2)`