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Question

If the velocity of light C, the universal gravitational constant G, and Planck's constant h are chosen as fundamental units, the dimension of mass in this system are

A
h1/2C1/2G1/2
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B
h1C1G
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C
hCG1
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D
hCG
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Solution

The correct option is B h1/2C1/2G1/2
Speed of light C=[LT1]
gravitational constant G=[M1L3T2]
planck's constant h=ML2T1

Let M=CxGyhz
[M]=[LT1]x[M1L3T2]y[ML2T1]z

[M]=[My+zLx+3y+2zTx2yz]

y+z=1,x+3y+2z=0,x2yz=0

On solving, we get
x=12;y=12;z=12
So, dimension of M=[C1/2G1/2h1/2]

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