If the velocity of light c, gravitational constant g and planck's constant h are chosen h as fundamental units, what are the dimensions of mass, length and time in the new system?
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You need to apply the principle of homogeneity for solving the problem. Principle of homogeneity states that in the correct equation, the dimensions of each term either subtracted or added must be same that is, dimensions of RHS and LHS should be equal.
The dimensions of mass m = kc^1/2 h^1/2 G ½ = k squareroot of ch/G. The dimensions of length L= kc^-3/2 h^1/2 G^1/2 = K sq.root of Hg/c^3. Dimension of time T = kc^-5/2 h^1/2 G^1/2 = k sq. root Hg/c^5.
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k = √Hg/c^5
hope this will help you
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