A thin rod of length `L` and mass `M` is bent at its midpoint into two halves so that the angle between them is `90^@`. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is.

Options

A. `(ML^(2))/(6)`
B. `(sqrt2ML^(2))/(24)`
C. `(ML^(2))/(24)`
D. `(ML^(2))/(12)`

Answer

D

Explanation

Length of each part `=(L)/(2)` and mass of each part `=(M)/(2)`
The M.l. of a rod about an axis passing through its end and perpendicular to its plane is `(1)/(3)ML^(2)`.
`therefore` For each part, `l=(1)/(3)((M)/(2))((1)/(2))^(2)=(1)/(24)ML^(2)`
`therefore` The net M.l. of the bent rod about an axis passing through B is `2xx(1)/(24)ML^(2)=(1)/(12)ML^(2)`