If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
${h^{1/2}}{c^{ - 3/2}}{G^{1/2}}$
${h^{1/2}}{c^{3/2}}{G^{1/2}}$
${h^{1/2}}{c^{ - 3/2}}{G^{ - 1/2}}$
${h^{ - 1/2}}{c^{ - 3/2}}{G^{1/2}}$
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
Let radius of gyration $[k] \propto {[h]^x}{[c]^y}{[G]^z}$
By substituting the dimension of $[k] = [L]$
$[h] = [M{L^2}{T^{ - 1}}],\,[c] = [L{T^{ - 1}}],\,[G] = [{M^{ - 1}}{L^3}{T^{ - 2}}]$
and by comparing the power of both sides
we can get $x = 1/2,\,y = - 3/2,\,z = 1/2$
So dimension of radius of gyration are ${[h]^{1/2}}{[c]^{ - 3/2}}{[G]^{1/2}}$
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