What is the moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end?

Explanation

The moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end is I.
The moment of inertia of such rod about an axis passing through its centre and perpendicular to the length is `I_(c)=(Ml^(2))/(12)`
`therefore` From theorem of parallel axis
`I=I_(c)+Md^(2)`
`therefore I=(Ml^(2))/(12)+(Ml^(2))/(4)[because d=(l)/(2)]`
`therefore I=(Ml^(2))/(3)" "......(1)`
Comparing equation (1) to `I=Mk^(2)`
`k^(2)=(l^(2))/(3)`
`therefore` Radius of gyration `k=(l)/(sqrt(3))`