Match the SI base quantities in List I with the expressions in List II.
List I:
A. Metre (L)
B. Second (T)
C. Kilogram (M)
D. Kelvin (K)
List II: I. √(hc/G) II. √(Gh /c⁵) III. √(K²L²c³ /Gh) IV. √(Gh /c³)
Here h is Planck's constant, G is the universal gravitational constant and c is the speed of light in vacuum. Choose the correct matching.

Question

Match the SI base quantities in List I with the expressions in List II.

List I:
A. Metre (L)
B. Second (T)
C. Kilogram (M)
D. Kelvin (K)

List II: I. √(hc/G) II. √(Gh /c⁵) III. √(K²L²c³ /Gh) IV. √(Gh /c³)

Here h is Planck's constant, G is the universal gravitational constant and c is the speed of light in vacuum. Choose the correct matching.

G1 Physics · Accepted Answer

The dimensions of the stated constants are [h] = M L² T⁻¹, [c] = L T⁻¹, [G] = M⁻¹ L³ T⁻². For List-II item I: √(hc ÷ G) = √[(M L² T⁻¹)(L T⁻¹) ÷ (M⁻¹ L³ T⁻²)] = M. Therefore I represents kilogram. For item II: √(Gh ÷ c⁵) = T. Therefore II represents second. For item IV: √(Gh ÷ c³) = L. Therefore IV represents metre. For item III, retaining the dimensional symbols K and L exactly as written in the question: √(K²L²c³ ÷ Gh) = K. Therefore III represents kelvin. Hence the correct matching is A → IV,…