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. `c^(2)[G (e^(2))/(4 pi epsilon_(0))]^(1//2)`
B. `(1)/(c^(2))[G (e^(2))/(G4 pi epsilon_(0))]^(1//2)`
C. `(1)/(c ) G (e^(2))/(4 pi epsilon_(0))`
D. `(1)/(c^(2))[G (e^(2))/(4 pi epsilon_(0))]^(1//2)`

Answer

d

Explanation

`[L] = [e] ^(0) [G]^(1) [(e^(2))/( 4 pi epsilon_(0))]^(2)`
`[L] = [LT^(-1)]^(a) [M^(-1)L^(3)T^(-2)]^(b) [ML^(3)T^(c)]`
`[L] = [L^(a+3b+3c)M^(-b+c)T^(-a-2b-2c)]`
`a + 3b + 3c = 1 - b + c = 0`
`a + 2b +2c = b`
On solving `a= -2, b= (1)/(2) ,c=(1)/(2)`
`:. L = (1)/(c^(2))[G.(e^(2))/(4piepsi_0)]^(1/2)`