The dimensions of the area A of a black hole can be written in terms of the universal constant G, its mass M and the speed of light c as $A = G^{α} M^{β} c^{γ}$ . Here

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Solution

The correct option is B
$A = G^{α} M^{β} c^{γ} L^{2} = (M^{- 1} L^{3} T^{- 2})^{α} (M^{1})^{β} (L^{1} T^{- 1})^{γ} By comparing - α + β = 0........... (1) 3 α + γ = 0........... (2) - 2 α - γ = 0.......... (3)$
By solving (1),(2),(3)
$α = 2, β = 2, and γ = - 4$

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The dimensions of the area A of a black hole can be written in terms of the universal constant G, its mass M and the speed of light c as A=GαMβcγ. Here

The correct option is B A=GαMβcγL2=(M−1L3T−2)α(M1)β(L1T−1)γBy comparing−α+β=0...........(1)3α+γ=0...........(2)−2α−γ=0..........(3) By solving (1),(2),(3) α=2,β=2,and γ=−4

The dimensions of the area A of a black hole can be written in terms of the universal constant G, its mass M and the speed of light c as $A = G^{α} M^{β} c^{γ}$ . Here

The correct option is B
$A = G^{α} M^{β} c^{γ} L^{2} = (M^{- 1} L^{3} T^{- 2})^{α} (M^{1})^{β} (L^{1} T^{- 1})^{γ} By comparing - α + β = 0........... (1) 3 α + γ = 0........... (2) - 2 α - γ = 0.......... (3)$
By solving (1),(2),(3)
$α = 2, β = 2, and γ = - 4$