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