A uniform thin bar of mass 6 kg and length 2.4 m is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is ×10⁻¹ kg m².

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8. The bar becomes six equal sides: each of length a=(2.4)/6=0.4 m and mass m=6/6=1 kg. For a regular hexagon of side a, the perpendicular distance from the centre to the middle of a side is d=(a√3)/2, so d²=(3a²)/4. Each side, about the perpendicular axis through the centre of the hexagon: (ma²)/(12)+md²=(ma²)/(12)+(3ma²)/4. =ma²(1/(12)+9/(12))=(10ma²)/(12)=(5ma²)/6. Six sides: I=6×(5ma²)/6=5ma²=5(1)(0.4)²=5(0.16)=0.8 kg m². Written as asked: 8×10⁻¹ kg m².

A uniform thin bar of mass 6 kg and length 2.4 m is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is ______ ×10⁻¹ kg m².

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