Question

# Four thin rods of same mass $$M$$ and same length $$l$$, form a square as shown in the figure. Moment of inertia of this system about an axis passing through centre $$O$$ and perpendicular to plane is :

A
43MI2
B
MI23
C
MI26
D
23MI2

Solution

## The correct option is A $$\cfrac { 4 }{ 3 } M{ I }^{ 2 }$$Moment of inertia of rod $$AB$$ about$$P=\cfrac { 1 }{ 12 } M{ I }^{ 2 }\quad$$$$MI$$ of rod $$AB$$ about$$O=\cfrac { M{ I }^{ 2 } }{ 12 } +M{ \left( \cfrac { I }{ 2 } \right) }^{ 2 }=\cfrac { 1 }{ 3 } M{ I }^{ 2 }$$ (from the theorem of parallel axis)and the system consists of $$4$$ rods of similar type so by the symmetry$${ I }_{ system }=\cfrac { 4 }{ 3 } M{ I }^{ 2 }$$Physics

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