Check the following equation by dimensional analysis 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 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.