Question

test the dimensional consistency of equation E=m
${c}^{2}$


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Answer 1

Answer:

✨

α ƒєsτıναℓ ƒuℓℓ

Ŏƒ sωєєτ мємσяıєs,

sκy ƒuℓℓ σƒ light,

мσuτн ƒuℓℓ σƒ sωєєτs,

нσusє ƒuℓℓ σƒ đıyαs

αиđ

нєαяτ ƒuℓℓ σƒ jσy.

ωısнıиg..

❤нαppy đıωαℓı τσ yσu❤

αиđ

❤yσuя ƒαмıℓy❤

✨

Answer 2

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.