Arrive at Einstein's mass-energy relation by dimensional method (E = `mc^(2)`).

Explanation

Let us assume that the Energy E depends on mass m and velocity of light c.
`E prop m^(a)c^(b)`
`E = km^(a)c^(b)` where k is a constant
Dimensions of E = `[ML^(2)T^(-2)]`
Dimensions of m = [M]
Dimensions of c = `[LT^(-1)]`
Substituting the values in the above equation
`[ML^(2)T^(-2)] = K[M]^(a)[LT^(-1)]^(b)`
By equating the dimensions
a = 1 , b = 2
-b = -2
`E = k.mc^(2)`
The value of constant k = 1
`E = mc^(2)`. This is Einstein.s mass energy relation.