Question

A thin uniform rod of length 'L' and mass 'M' is bent at the middle point 'O' at an angle of 45° as shown in the figure. The moment of inertia of the system about an axis passing through 'O' and perpendicular to the plane of the bent rod, is ______.

विकल्प

• `"ML"^2/6`

• `"ML"^2/24`

• `"ML"^2/3`

• `"ML"^2/12`

Answer 1

A thin uniform rod of length 'L' and mass 'M' is bent at the middle point 'O' at an angle of 45° as shown in the figure. The moment of inertia of the system about an axis passing through 'O' and perpendicular to the plane of the bent rod, is `underline("ML"^2/12)`.

Explanation:

Moment of inertia of each half of the rod about the mid point is given by

`"I"_1=("M"/2("L"/2)^2)/3="ML"^2/24`

Total moment of inertia = I `2"I"_1="ML"^2/12`