State and explain the theorem of parallel axis with an example

Explanation

Statement : The moment of inertia of body about any axis is equal to the sum of the moment of inertia of the body about an parallel axis passing through the centre of mass and the product of mass of the body and square of the distance between the two parallel axis.
`i=I_0+Md^2` Let 'd' be the distance between the two parallel axes. Let `I_0` be the moment of inertia about an axis passing through the centre of mass of a thin rod of length L.
We know that `I_0=(ML^2)/(12)` and `d=L/2`
Hence moment of inertia at one end `=(ML^2)/(12)+M(L/2)^2`
`I=(ML^2)/(4)[1/3+1]=(ML^2)/(3)`