The equation E=mc^2, given by Albert Einstein is the most significant one in the atomic level which paved the way for nuclear reactors, the future energy source to human being.Many people doubt this equation, but it can be solved by simple dimensional analysis.

Dimensional analysis is the simplest way to analyze whether the equation is dimensionally correct or not.

Basically it is based on three dimensions, namely mass(M), length(L), and time(T).

Let 'E' be the ..........L.H.S &

mc^2 be the ............R.H.S

'E' refers to energy, which has the dimension of Force multiplied by displacement.According to newton, F=ma,

Where 'm' has the dimension of mass denoted by M and 'a' is given by velocity by time, which has the dimension of LT^-2.Hence the dimension of 'F' is MLT^-2.Therefore

Now, in R.H.S the dimension of 'm' is given by M and the dimension of 'c^2' is given by L^2T^-2, since 'c' has the dimensions of velocity.Therefore

It is seen that the dimension of 'E' is same as the dimension of mc^2 from the underlined words.

Therefore, L.H.S=R.H.S... Hence proved.

Dimensional analysis is the simplest way to analyze whether the equation is dimensionally correct or not.

Basically it is based on three dimensions, namely mass(M), length(L), and time(T).

**Dimensional analysis of E=mc^2 :**Let 'E' be the ..........L.H.S &

mc^2 be the ............R.H.S

'E' refers to energy, which has the dimension of Force multiplied by displacement.According to newton, F=ma,

Where 'm' has the dimension of mass denoted by M and 'a' is given by velocity by time, which has the dimension of LT^-2.Hence the dimension of 'F' is MLT^-2.Therefore

__the dimension of 'E' is ML^2T-2__, as in the first statement.Now, in R.H.S the dimension of 'm' is given by M and the dimension of 'c^2' is given by L^2T^-2, since 'c' has the dimensions of velocity.Therefore

__the dimensions of 'mc^2' is ML^2T^-2__.It is seen that the dimension of 'E' is same as the dimension of mc^2 from the underlined words.

Therefore, L.H.S=R.H.S... Hence proved.

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