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

Answer

B

Explanation

Moment of inertia of a rod about an axis passing through its centre and perpendicular to the rod is , `I _(1) = ( ML ^(2))/( 12)`
In given situation, `d = (L )/(2) - (L)/(3) `
`implies d = (L)/(6)`
Using parallel axis theorem,
`I _(2) = I_(1) + Md ^(2)`
`implies I _(2) = ( M L ^(2))/( 12) + M ((L )/(6)) ^(2)`
`implies I _(2) = ( ML ^(2))/( 12) + ( ML ^(2))/( 36)`
`implies I _(2) =( ML ^(2))/(9)`