where (Planck’s constant), (gravitational constant) and (speed of light in vacuum) as fundamental units. [2026]

Question

Match List-I with List-II.

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: [2026]

Smart Achievers · Accepted Answer

(2)

$[h] = [M L^{2} T^{- 1}]$

$[c] = [L T^{- 1}] and [G] = [M^{- 1} L^{3} T^{- 2}]$

$then [\sqrt{\frac{h c}{G}}] = {[\frac{M L^{2} T^{- 1} L T^{- 1}}{M^{- 1} L^{3} T^{- 2}}]}^{1 / 2} = [M]$

$[\sqrt{\frac{G h}{c^{5}}}] = {[\frac{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}{L^{5} T^{- 5}}]}^{1 / 2} = [T]$

$[\sqrt{\frac{K^{2} L^{2} c^{3}}{G h}}] = {[\frac{K^{2} L^{2} L^{3} T^{- 3}}{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}]}^{1 / 2} = [K]$

$[\sqrt{\frac{G h}{c^{3}}}] = {[\frac{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}{L^{3} T^{- 3}}]}^{1 / 2} = [L]$

$A→IV, B→II, C→I, D→III$

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