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^(0)`
B. `h^(2) e G^(0) mu`
C. `h^(0)e^(2) G^(-1) mu`
D. `he^(-2) mu^(0)`

Answer

A

Explanation

Here `v = e^(a) h^(b) mu^( c ) G^(d) `. Taking the dimensions, `M^(0) LT^(-1) A^(0)`
` = [AT^(1)] ^(a) [ML^(2) T^(-1) ]^(b) [ MLT^(-2) A^(-2)]^( c ) [ M^(-1) L^(3) T^(-2) ]^(d)`
There will be four simultaneous equations by equating the dimensions of `M,L , T, and , A`. These are ` a-2c = 0 , a - b - 2c -2d = -1 , b+ c - d = 0 and 2b + c + 3d = 1`.
Solving for `a , b , c and d`, we get
` a = -2 , b = 1 , c = -1 , d = 0`
Thus , `v = e^(-2) h mu^(-1) G^(0)`