If the velocity of light c,

Question:

If the velocity of light c, Planck’s constant h and gravitational constant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

Solution:

Principle of homogeneity is used for solving this problem.

[h] = [ML2T1] [c] = [LT-1] [G] = [M-1L3T-2]

Let m = kcahbGc

Solving the above we get,

m = kc1/2h1/2G-1/2 = k√ch/G

Let L = kcahbGc

Solving the above we get,

L = kc-3/2h1/2G1/2 = k√hG/c3

Let T = cahbGc

Solving the above we get,

L = kc-5/2h1/2G1/2 = k√hG/c5

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