A physical quantity of the dimensions of length that can be formed out of c, G and $$e24$$πε$$0is$$ [c is velocity of light, G is universal constant of gravitation and e is charge]:

Correct option is 41c2[Ge24πε0]12

Questions

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4 {πε}_{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]:

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c2[Ge24πε0]12

1c2[e2G4πε0]12

1cGe24πε0

1c2[Ge24πε0]12

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detailed solution

Correct option is D

[L] = [c]a[G]b[e24πε]c[L] = [LT-1]a[M-1L3T-2]b[ML3T-2]c[L] = La+3b+3cM-b+cT-a-2b-2ca+3b+3c = 1-b+c = 0a+2b+2c = 0on solving, a = -2b, b = 12,c = 12∴ L = 1c2[G.e24πε0]12

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A physical quantity of the dimensions of length that can be formed out of c, G and e24πε0is [c is velocity of light, G is universal constant of gravitation and e is charge]:

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A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4 {πε}_{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]: