JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
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
- A \(\frac{{ch}}{{2\pi \varepsilon _0^2}}\)
- B \(\frac{{{e^2}}}{{2\pi {\varepsilon _0}Gm_e^2}}\)
- C \(\frac{{{\mu _0}{\varepsilon _0}G}}{{{c^2}h{e^2}}}\)
- D \(\frac{{2\pi \sqrt {{\mu _0}{\varepsilon _0}} h}}{{c{e^2}G}}\)
Answer & Solution
Correct Answer
(B) \(\frac{{{e^2}}}{{2\pi {\varepsilon _0}Gm_e^2}}\)
Step-by-step Solution
Detailed explanation
\begin{array}{l} The\,{\rm{Dimensional}}\,{\rm{formulae}}\,{\rm{of}}\\ {\rm{e}}\,{\rm{ = }}\left[ {{M^0}{L^0}{T^1}{A^1}} \right]\\ {\varepsilon _0} = \left[ {{M^{ - 1}}{L^{-3}}{T^4}{A^2}} \right]\\ G = \left[ {{M^{ - 1}}{L^3}{T^{ - 2}}} \right]\\ and\,{m_e} = \left[…
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