A physical energy of the dimension of length that can be formula cut of `c,G` and `(e^(2))/(4 pi epsilon_(0))` is [`c` is velocity of light `G` is universal constant of gravilation e is change

Options

A. `1/c^2[G(e^2)/(4piin_0)]^(1//2)`
B. `c^2[G(e^2)/(4piin_0)]^(1//2)`
C. `1/c^2[G(e^2)/(G4piin_0)]^(1//2)`
D. `1/c G(e^2)/(4piin_0)`

Answer

A

Explanation

`[L]=[c]^(a) [G]^(b) [e^2/(4piepsilon_0)]^(c)`
`[L] =[LT^(-1)]^(a)[M^(-1)L^(3) T^(2)]^(b)[ML^(3)T^(-2)]^c`
`[L] = L^(a+3b+3c) M^(-b+c)T^(-a-2b-2c)`
`a + 3b + 3c = 1`
`-b + c = 0 , -a - 2b - 2c = 0`
On solving, `a =-2, b=1/2 , c =1/2`
`:. L =1/c^2 [G.(e^2)/(4piepsilon_0)]^(1/2)`