[c А physical quanlity of dimensions of length that can be formed out of c ,G and e2/4pie eo is (c is velocity of light,G is universal constant of gravitation and e is charge)
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Given,
C,G,
4πε
0
e
2
So,
[L]=[C]
a
,[G]
b
[
4πε
0
e
2
]
c
[L]=[LT
−1
]
a
,[ML
3
T
−2
]
b
[ML
3
T
−2
]
c
[L]=L
a+3b+3c
M
−b+c
T
−a−2b−2c
on comparing we get,
a=3b+3c=1,
−b+c=0
a+2b+2c=0
On solving we get,
a=−2,b=
2
1
,c=
2
1
Thus,
L=
C
2
1
[
4πε
0
Ge
2
]
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