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(B) physical quantity has the same value in different systems of units if it is dimensionless. We check the dimensions of the given expression $\frac{

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$\frac{e^2}{2\pi \varepsilon _0 G m_e^2}$

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(B) physical quantity has the same value in different systems of units if it is dimensionless. We check the dimensions of the given expression $\frac{e^2}{2\pi \varepsilon _0 G m_e^2}$.The dimensions of the constants are:$e = [M^0 L^0 T^1 A^1]$$\varepsilon _0 = [M^{-1} L^{-3} T^4 A^2]$$G = [M^{-1} L^3 T^{-2}]$$m_e = [M^1 L^0 T^0]$Substituting these into the expression:$\frac{[T^2 A^2]}{[M^{-1} L^{-3} T^4 A^2] [M^{-1} L^3 T^{-2}] [M^2]} = \frac{[T^2 A^2]}{[M^{-1-1+2} L^{-3+3} T^{4-2} A^2]} = \frac{[T^2 A^2]}{[M^0 L^0 T^2 A^2]} = 1$Since the expression is dimensionless,its value remains constant across all systems of units.

From the following combinations of physical constants (expressed through their usual symbols),the only combination that would have the same value in different systems of units is:

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