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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 h1/2C1/2G−1/2Speed of light C=[LT−1]gravitational constant G=[M−1L3T−2]planck's constant h=ML2T−1Let M=CxGyhz[M]=[LT−1]x[M−1L3T−2]y[ML2T−1]z[M]=[M−y+zLx+3y+2zT−x−2y−z]−y+z=1,x+3y+2z=0,−x−2y−z=0On solving, we getx=12;y=−12;z=12So, dimension of M=[C1/2G−1/2h1/2]

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