Question 62 of 280

A uniform thin bar of mass $6kg$ and length $2.4$ meter 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 hexagon is ___________ $\times {10}^{-1}kg{m}^{2}.$

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Answer: 8

$61=2.4$ $\ell =0.4m$
$\sin 60^{\circ}=\dfrac{r}{\ell }$
$r=1\sin 60^{\circ}=\dfrac{\ell \sqrt{3}}{2}$
MOI, $I=\left[\dfrac{m{\ell }^{2}}{12}+m{r}^{2}\right]6$
$=\left[\dfrac{m{\ell }^{2}}{12}+m{\left(\dfrac{\ell \sqrt{3}}{2}\right)}^{2}\right]6$
$=5m{l}^{2}$
$=5\times 1\times 0.16$
$=0.8$
$I=8\times {10}^{-1}kg{m}^{2}$