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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 c1/2h1/2G−1/2Dimensions of velocity of Light c-- LT−1Dimensions of gravitational constant G -- L3M1T2Dimensions of planck's constant h -- ML2T1Let a,b and c be powers of c,G and h respectively such that their product gives dimensions of mass.caGbhc=(LT−1)a×(L3M1T2)b×(ML2T1)c=M1L0T0on solving,a=1/2, b=−1/2, c=1/2.Hence, Option B is correct.

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