If the velocity of light c, universal gravitational constant G and Planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is: (a) [h¹c¹G⁻¹] (b) [h-1/2c1/2G1/2] (c) [h1/2c1/2G-1/2] (d) [h1/2c-1/2G¹]

Answer: (c). [h] = [ML²T⁻¹], [c] = [LT⁻¹], [G] = [M⁻¹L³T⁻²]. [hc/G] = [ML³T⁻²][M⁻¹L³T⁻²] = [M²]. Mass = √(hc/G) = [h1/2c1/2G-1/2]. So the answer is (c).

If the velocity of light c, universal gravitational constant G and… | JEE Main 2023 (1 Feb, Shift 2)

Q28JEE Main 2023 · 1 FEB · SHIFT 2Easy

Applications of Dimensional Analysis

If the velocity of light $\mathrm{c}$ , universal gravitational constant $\mathrm{G}$ and Planck's constant $\mathrm{h}$ are chosen as fundamental quantities. The dimensions of mass in the new system is:

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Answer: (c)

$[h] = [ML^2T^{-1}]$ , $[c] = [LT^{-1}]$ , $[G] = [M^{-1}L^3T^{-2}]$ .
$[hc/G] = \dfrac{[ML^3T^{-2}]}{[M^{-1}L^3T^{-2}]} = [M^2]$ .
Mass $= \sqrt{hc/G} = [h^{1/2}c^{1/2}G^{-1/2}]$ .
So the answer is (c).

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