Question

If the velocity of light c,gravitational constant G and planck's constant h are chosen as fundamental units the dimension of length L in the new system is

Answer 1

hope it will help you and please comment if I had done any type of mistake so that I can improve it.

Answer 2

Hey Dear,

● Answer -

[L] = [G]^(1/2) [h]^(1/2) [c]^(-3/2)

● Explanation -

Let's first recollect the known dimensions -

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

[G] = [L3M-1T-2][h] = [L2M1T-1]

[G] = [L3M-1T-2][h] = [L2M1T-1][c] = [L1T-1]

Now, lets calculate dimensions of length -

[L] = [G]^x [h]^y [c]^z

[L] = [L3M-1T-2]^x [L2M1T-1]^y [L1T-1]^z

[L1M0T0] = [L]^(3x+2y+z) [M]^(-x+y) [T]^(-2x-y-z)

Comparing indexes on both sides -

1 = 3x + 2y + z

0 = -x + y

0 = -2x - y - z

Solving these equations, we get

x = 1/2

x = 1/2y = 1/2

x = 1/2y = 1/2z = -3/2

Therefore, dimensions of length in mew system will be -

[L] = [G]^(1/2) [h]^(1/2) [c]^(-3/2)

Hope this helps you..