If the constant of gravitation \langle G \rangle , Planck's…

Physics Units, Dimensions and Measurement Mix Single Correct MCQ

Published on: September 12, 2026

If the constant of gravitation \langle G \rangle , Planck's constant \{j\} 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^{1/2} G^{-1/2}

h^{1/2} c^{-3/2} G^{1/2}

Text Solution

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The correct answer is:

Let radius of gyration [k], [h]^r [c]^v [G]^2

By substituting the dimension of [k] = [l]

[\hbar] = [ML^{2}T^{-1}], [c] = [LT^{-1}], [G] = [M^{-1}L^{3}T^{-2}]

and by comparing the power of both sides

we can get \(x \quad \frac{1}{2}, y \quad -\frac{3}{2}, z \quad \frac{1}{2}\)

So dimension of radius of gyration are \(\left[h\right]^{1/2} \left[c\right]^{1/2} \left[G\right]^{1/2}\)

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