The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G, its mass M and the speed of light c as `A=G^(alpha)M^(beta)c^(gamma)`. Here -

Options

A. `alpha = -2,beta = -2 and gamma = 4`
B. `alpha = 2,beta = 2 and gamma = -4`
C. `alpha = 3,beta = -3 and gamma = -2`
D. `alpha = -3,beta = -3 and gamma = 2`

Answer

B

Explanation

`A = G^(alpha)M^(beta)c^(gamma)`
`L^2=(M^(-1)L^3T^(-2))^(alpha)(M^1)beta(L^1T^(-1))^(gamma)`
`-alpha+beta =0 " "....(i) `
`3alpha+ gamma =2 " "...(ii)`
`-2 alpha - gamma = 0 " "....(iii)`
`alpha =2 , beta = 2 and gamma =-4`