If the speed of light c, universal gravitational constant G and Planck constant h are chosen as fundamental quantities, the dimension of mass is:
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Question

If the speed of light c, universal gravitational constant G and Planck constant h are chosen as fundamental quantities, the dimension of mass is:

G1 Physics · Accepted Answer

Let: M ∝ hˣcʸGᶻ Dimensions: [h] = ML²T⁻¹ [c] = LT⁻¹ [G] = M⁻¹L³T⁻² Therefore: M¹L⁰T⁰ = Mˣ⁻ᶻ L²ˣ⁺ʸ⁺³ᶻ T⁻ˣ⁻ʸ⁻²ᶻ Comparing powers: x − z = 1 2x + y + 3z = 0 −x − y − 2z = 0 Solving: x = 1/2 y = 1/2 z = −1/2 Hence: M ∝ h¹ᐟ²c¹ᐟ²G⁻¹ᐟ² Hence option D.