Planck's constant h, speed of light in vacuum c and Newton's gravitational constant G are fundamental constants. Which combination has the dimension of length?
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Question

Planck's constant h, speed of light in vacuum c and Newton's gravitational constant G are fundamental constants. Which combination has the dimension of length?

G1 Physics · Accepted Answer

Step 1: Let L=hᵃcᵇGᶜ. Step 2: Using [h]=[ML²T⁻¹], [c]=[LT⁻¹] and [G]=[M⁻¹L³T⁻²], equating powers for length gives a=c=1/2 and b=−3/2. Step 3: Hence L=√(hG)/c³ᐟ². Final: Option A.