The moment of inertia of a rod about an axis through its centre and perpendicular to it is `(1)/(12)ML^(2)` (where M is the mass and L, the length of the rod). The rod is bent in the middle so that the two halves make an angle `60^(@)`. The moment of inertia of the bent rod about the same axis would be..........

Options

A. `(1)/(48)ML^(2)`
B. `(1)/(12)ML^(2)`
C. `(1)/(24)ML^(2)`
D. `(ML^(2))/(8sqrt(3))`

Answer

B

Explanation

Moment of inertia of uniform rod about one end = `(ML^(2))/(3)`
Moment of inertia of a rod about an axis passing through O and perpendicular to the plane of the rod will be
`I.=2((M)/(2))(((L)/(3))^(2))/(3)`
`=(ML^(2))/(4xx3)`
`therefore I.=(ML^(2))/(12)`