If gravitational constant G , planks constant h and speed of light c considered as fundamental physical quantities then find dimensional formula of time

Question

If gravitational constant G , planks constant h and speed of light c considered as fundamental physical quantities then find dimensional formula of time, G 1 2 h 1 2 c - 5 2, G 1 h 2 c - 5 2, G 1 2 h 1 2 c - 2, G 2 h 1 2 c - 2

MARKS App · Accepted Answer

Let T = G α L β C γ = M - 1 L 3 T - 2 9 ⋅ M L 2 T - 1 β L T - 1 γ ⇒ - α + β = 0 3 ∝ + 2 β + γ = 0 - 2 α - β - γ = 1 On solving we get α = 1 2 , β = 1 2 , γ = 5 2

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