Calculate the moment of inertia of a uniform rod of mass `M` and length `l` about an axis passing through an end and perpendicular to the rod. The rod can be divided into a number of mass elements along the length of the rod.

Explanation

For the rod of mass `M` and length `l`, moment of inertia about an axis `AB`, Fig.

`I_(AB) = (M l^(2))/(12)`
The given axis is `XY`. Applying theorem of parellel axes,
`I_(XY) = I_(AB) + M(l//2)^(2)`
`I_(XY) = (Ml^(2))/(12) + (Ml^(2))/(4) = (Ml^(2))/(3)`