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, 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^(p)h^(q)c^(r)` ….(i)
`[M^(1)L^(2)T^(-2)]= [M^(-1)L^(3)T^(-2)]^(p)[ML^(2)T^(-1)]^(q)[LT^(-1)]^(r)= [M^(-p+q)L^(3p+2q+r)T^(-2p-q-r)]`
Applying principle of homogeneity of dimensions we get
-p+q= 1 …(ii)
2p+2q+r=2
-2p-q-r=-2
Adding (iii) and (iv) we get p+q=0
adding (ii) and (v) we get `2q=1 , q= (1)/(2)`
From (ii) `p= q-1= (1)/(2)-1= -(1)/(2)`
Put in (iii) `-(3)/(2)+ 1+r= 2, r= (5)/(2)`