show that the Einsstien mass energy equation is dimensionally constant
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Explanation:
The question is asking if the dimensions of E=mc^2 are consistent… with what? The dimensions are internally consistent if the dimensions of E are the same as the dimensions of mc^2.
Why not do the dimensional analysis and see.
The dimensions of energy [E] are ML^2/T^2
The dimensions of mass [m] are M
The dimensions of the invariant speed [c] are those of velocity… L/T
Work it out.
Note:
The SI units of c^2 are (equivalent to) “Joules per kilogram”, making c^2 a conversion factor between units of mass and units of energy. Thus, since c is the same to all observers, the formula as saying that mass is a form of energy.
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