Dimensions of universal gravitational constant (G) in terms of Planck's constant (h) , distance (L) , mass (M) and time (T) are _______.

Step-by-step solution

The dimensional formula of the universal gravitational constant G is obtained from Newton's law of gravitation F = G m₁ m₂ r^2 . [G] = [F][r^2] [m₁ m₂] = [MLT⁻²][L^2] [M^2] = [M⁻¹L^3T⁻²] The dimensional formula of Planck's constant h is obtained from the energy of a photon E = h . [h] = [E] [ ] = [ML^2T⁻²] [T⁻¹] = [ML^2T⁻¹] Let the dimensions of G be expressed as [G] = [h]^a [L]^b [M]^c [T]^d . Substituting the dimensions, we get: [M⁻¹L^3T⁻²] = [ML^2T⁻¹]^a [L]^b [M]^c [T]^d [M⁻¹L^3T⁻²] = [M^ a+c L^ 2a+b T^ -a+d ] E