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Question

If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is            


  1. c1/2G1/2h-1/2
  2. c1/2G1/2h1/2
  3. c1/2G-1/2h1/2
  4. c-1/2G1/2h1/2


Solution

The correct option is C c1/2G-1/2h1/2

            Let mcxGyhz
by substituting the following dimentions :
[c] = LT1; [G] = [M1L3T2] and [h] = [ML2T1]
Now comparing both sides we will get
x = 12; y=12,z=+12
So mc12 G12 h12

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