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Question

If C the velocity of light, h Planck's constant and G Gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is:

A
h1/2G1/2C0
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B
h1/2C1/2G1/2
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C
h1/2C1/2G1/2
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D
h1/2C1/2G1/2
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Solution

The correct option is B h1/2C1/2G1/2
Dimensional formula for, h=[ML2T1]
Dimensional formula for, G=[M1L3T2]
Dimensional formula for, C=[LT1]

Let mass be represented as: m=haGbCc
[M]= [ML2T1]a [M1L3T2]b [LT1]c

[M]= [MabL2a+3b+cT(a+2b+c)]

On comparing we get:
ab=1 .........(1)
2a+3b+c=0 .........(2)
a+2b+c=0 .........(3)

Subtracting (3) from (2) we get:
a+b=0
b=a ...........(4)

Solving (1) and (4):
a=12 b=12

From (3),
12+2×12+c=0
c=12
[m]=[h1/2G1/2C1/2]

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