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Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
- √(Gh/c⁵)
- √(hc⁵/G)
- √(Gh/c³)
- √(c³/Gh)
Correct answer: √(Gh/c⁵)
Solution
With [G]=M^-1 L^3 T^-2, [h]=M L^2 T^-1, [c]=L T^-1: Gh = L^5 T^-3, and Gh/c^5 = L^5 T^-3 / (L^5 T^-5) = T^2. So time ~ sqrt(Gh/c^5) (the Planck time).
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