Match List-I with List-II. List-I List-II A. Meter (L) I. hc G B. Second (S) II. Gh c^5 C. Kilogram (M) III. K^2L^2c^3 Gh D. Kelvin (K) IV. Gh c^3 where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units. Choose the correct answer from the options given below :

Step-by-step solution

The dimensional formulas for the given fundamental constants are: [h] = M L^2 T⁻¹ [c] = L T⁻¹ [G] = M⁻¹ L^3 T⁻² Evaluating the dimensions of the expressions in List-II: For I: hc G = (M L^2 T⁻¹)(L T⁻¹) M⁻¹ L^3 T⁻² = M^2 = M (Kilogram). Thus, C I. For II: Gh c^5 = (M⁻¹ L^3 T⁻²)(M L^2 T⁻¹) (L T⁻¹)^5 = L^5 T⁻³ L^5 T⁻⁵ = T^2 = T (Second). Thus, B II. For IV: Gh c^3 = (M⁻¹ L^3 T⁻²)(M L^2 T⁻¹) (L T⁻¹)^3 = L^5 T⁻³ L^3 T⁻³ = L^2 = L (Meter). Thus, A IV. For III: Substituting L^2 = Gh c^3 from IV into the expression gives K