A physical quantity of the dimensions of length that can be formed out of c , G and e^2/4π_0 is: - Physics MCQ NEET (UG) 2017 2026 | ExamTest.live

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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 π ε _{0}} is:

Solution & Step-by-step Explanation

Let X = \frac{e ^{2}}{4 π ε _{0}} . Dimensions of X : [M L^{3} T^{- 2}] (from F = X / r^{2}).Dimensions of G : [M^{- 1} L^{3} T^{- 2}] .Dimensions of c : [L T^{- 1}] .Let L = c^{x} G^{y} X^{z} . [L] = [L T^{- 1}]^{x} [M^{- 1} L^{3} T^{- 2}]^{y} [M L^{3} T^{- 2}]^{z} Mass: - y + z = 0 ⟹ y = z .Time: - x - 2 y - 2 z = 0 ⟹ x = - 4 y .Length: x + 3 y + 3 z = 1 ⟹ - 4 y + 3 y + 3 y = 1 ⟹ 2 y = 1 ⟹ y = 1/2 .Thus z = 1/2 and x = - 2 . L = c^{- 2} (GX)^{1/2} = \frac{1}{c ^{2}} G \frac{e ^{2}}{4 π ε _{0}} .

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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 π ε _{0}} is:

\frac{1}{c ^{2}} [G \frac{e ^{2}}{4 π ε _{0}}]^{1/2}

c^{2} [G \frac{e ^{2}}{4 π ε _{0}}]^{1/2}

\frac{1}{c ^{2}} G \frac{e ^{2}}{4 π ε _{0}}

G \frac{e ^{2}}{4 π ε _{0} c}

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