Which of the following product of `e , h , mu , G` ( where ` mu` is permeability ) be taken so that the dimensions of the product are same as that of the speed of light ?

Options

A. `he^(-2)mu^(-1)G^(@)`
B. `h^(2)eG^(@)mu`
C. `h^(2)e^(2)G^(-1)mu`
D. `hGe^(-1)m^(e)`

Answer

A

Explanation

`v=e^(a)h^(b)mu^(c)G^(d)," "(AT)(a)(ML^(2)T^(-1))^(b)(MLT^(-2)A^(-2))^(c)(M^(-1)L^(3)T^(-2))^(d)`
`a-2c=0,a-b-2c-2d=-1,2b+c+3d=1,b+c-d=0`
`a=-2,b=1,c=-1,d=0," "v=e^(-2)h mu^(-1)G^(@)`