First slide

Dimensions of physical quantities

Question

If the velocity of light C, the universal gravitational constant G, and Planck's constant h are chosen as fundamental units, the dimensions of mass in this system are

Moderate

A

$h^{1 / 2} C^{1 / 2} G^{- 1 / 2}$
B

$h^{- 1} C^{- 1} G$
C

$h C G^{- 1}$
D

$hCG$

Solution

$\begin{array}{l} h = [M L^{2} T^{- 1}], G = [M^{- 1} L^{3} T^{- 2}], C = [L T^{- 1}] \\ ∴ h^{1 / 2} G^{- 1 / 2} C^{1 / 2} = M^{1 / 2} L T^{- 1 / 2} \times M^{1 / 2} L^{- 3 / 2} T^{1} \times L^{1 / 2} T^{- 1 / 2} \\ = M L^{0} T^{0} = Mass \end{array}$

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