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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 ______.
Options
`"ML"^2/6`
`"ML"^2/24`
`"ML"^2/3`
`"ML"^2/12`
MCQ
Fill in the Blanks
Solution
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`
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Moment of Inertia as an Analogous Quantity for Mass
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