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Question

If the velocity of light c, gravitational constant G, and Planck's constant h be taken as fundamental units, the dimension of mass in the new system will be :

A
c1/2h1/2G1/2
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B
c1/2h1/2G1/2
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C
c3/2h1/2G1/2
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D
c3/8h1/2G1/2
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Solution

The correct option is C c1/2h1/2G1/2
Dimensions of velocity of Light c-- LT1
Dimensions of gravitational constant G -- L3M1T2
Dimensions of planck's constant h -- ML2T1
Let a,b and c be powers of c,G and h respectively such that their product gives dimensions of mass.
caGbhc=(LT1)a×(L3M1T2)b×(ML2T1)c=M1L0T0
on solving,
a=1/2, b=1/2, c=1/2.
Hence, Option B is correct.

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