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))/(4piepsi_(0))]^((1)/(2))`
B. `c^(2)[G(e^(2))/(4piepsi_(0))]^((1)/(2))`
C. `(1)/(c^(2))[(e^(2))/(G4piepsi_(0))]^((1)/(2))`
D. `(1)/(c)G(e^(2))/(4 pi epsi_(0))`

Answer

A

Explanation

Let `(e^(2))/(4pi epsi_(0))=A=ML^(3)T^(-2)`
` l=C^(x)G^(y)(A)^(z)`
`L=[LT^(-1)]^(x)[M^(-1)L^(3)T^(-2)]^(y)[ML^(3)T^(-2)]^(z)`
`-y+z=0 implies y =z`.....(i)
`x+3y+3z=1`.....(ii)
`-x-4z=0`.......(iii)
From (i) , (ii) & (iii)
`z=y=(1)/(2),x=-2`