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A uniform thin rod of length $4l$ , mass 4m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O & perpendicular to the plane of the paper.
Option: 1
$\frac{m\: l^{2}}{3}$

Option: 2
$\frac{10m\: l^{2}}{3}$

Option: 3
$\frac{m\: l^{2}}{12}$

Option: 4
$\frac{m\: l^{2}}{24}$

Answers (1)

best_answer

Moment of inertia of uniform rod of length( $l$ ) -

$I= \frac{Ml^{2}}{12}$

About axis passing through its centre & perpendicular to its length.

The given structure can be broken into 4 parts

For $AB:I=I_{CM}+m\times d^{2}=\; \frac{ml^{2}}{12}+\frac{5m}{4}l^{2}\; ;\; I_{AB}=\frac{4}{3}ml^{2}$

For BO : $I=\frac{ml^2}{3}$

For composite frame : (by symmetry)

$I=2\left [ I_{AB}+I_{OB} \right ]=2\left [ \frac{4ml^{2}}{3}+\frac{ml^{2}}{3} \right ]=\frac{10}{3}ml^{2}.$

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Gunjita

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