The moment of inertia of a straight thin rod of mass M and length l about an axis perpendicular to its length and passing through its one end, is

Explanation

For the rod of mass M and length l, `I=Ml^(2)//12`. Using the parallel axes theorem. `I'=I+Ma^(2)` with `a=l//2` we get,
`I'=M(l^(2))/(12)+M((l)/(2))^(2)=(Ml^(2))/(3)`
We can check this independently since I is half the moment of inertia of a rod of mass 2 M and length 2l about its midpoint,
`I'=2M.(4l^(2))/(12)xx(1)/(2)=(Ml^(2))/(3)`