The moment of inertia of a uniform thin rod of length `L` and mass `M` about an axis passing through a point at a distance of `L//3` from one of its ends and perpendicular to the rod is

Options

A. `(7ML^(2))/(48)`
B. `(ML^(2))/(9)`
C. `(ML^(2))/(12)`
D. `(ML^(2))/(3)`

Answer

B

Explanation

`I=I_(CM)+M((L)/(2)-(L)/(3))^(2)`
= `(ML^(2))/(12)+M((3L-2L)/(6))^(2)`
= `(ML^(2))/(12)+(ML^(2))/(36)=(3ML^(2)+ML^(2))/(36)=(1)/(9)ML^(2)`