Question

a physical quantity of the dimensions of length that can be formed out of c, G and e^2/4π£o is ​( c is velocity of light G is universal constant of gravitation and e is charge)​

Answer 1

Answer:

Explanation: hope so it's related to question but you can do it easily by going through this solution

Answer 2

Dear Student,

◆ Answer -

X = k c^(-2) G^(1/2) (e²/4πε0)^(1/2)

● Explanation -

Let X be supposed physical quantity such that -

[X] = [c]^x.[G]^y.[e²/4πε0]^z

We know that dimensions are -

[X] = [L]

[c] = [L1T-1]

[G] = [L3M-1T-2]

[e²/4πε0] = [L5M1T-2]

So now,

[L] = [L1T-1]^x.[L3M-1T-2]^y.[L3M1T-2]^z

[L] = [L^(x+3y+3z).M^(-y+z).T^(-x-2y-2z)]

Comparing indices on two sides,

x + 3y + 3z = 1

-y + z = 0

-x - 2y - 2z = 0

Solving this,

x = -2

y = 1/2

z = 1/2

So supposed physical quantity is -

X = k c^(-2) G^(1/2) (e²/4πε0)^(1/2)

Thanks dear....