Question

check the correctness of equation of E=mc² using the dimensional analysis method

Answer 1

The dimensions of E m and c²....
$e = {m}^{1} {l}^{2} {t}^{ -2}$
$m = {m}^{1}$
${c}^{2} = {l}^{2} {t}^{ - 2}$
mc²→

$( {m}^{1} )( {l}^{2} {t }^{ - 2} ) \\ = (m {l}^{2} {t}^{ - 2} )$
which is same as the dimensions of E.
So the equation is Dimensionally Correct.

Hope it helps...
Regards,
Leukonov.