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

Step-by-step solution

E=G^p h^q c^r aligned & [ 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 ^ 3 p+2 q+r ~T ^ -2 p-q-r aligned Applying principle of homogeneity of dimensions, we get aligned & -p+q=1 & 3 p+2 q+r=2 & -2 p-q-r=-2 aligned 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=- 1 2 . Put in (iii), we get - 3 2 +1+r=2, r=5 / 2