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 `

Answer

A

Explanation

`E=G^(n) h^(n) c^(r)`.......(i)
`[M^(1)L^(2)T^(-2)]=[M^(-1)L^(3)T^(-2)]^(n) [ML^(2)T^(-1)]^(n)[LT^(-1)]^(r)`
`=M^(p)""^qL^(3p+2q+r)T^(-2p) qr`
Applying principle of homogeneity of dimensions, we get
`-p+q=1......(i)`
`3p+2q+r=2......(iii)`
`-2p-q-r=-2......(iV)`
Add (iii) and (iv), p+q=0
Add (ii) and (v), we get `q=(1)/(2)`
From (ii)(, we get `p=q-1=1/2 =-1/2`
Put in (iii), we get `-3/2+1+r=2, r5//2`