<math> <mi>A</mi> <mi>B</mi> <mi>C</mi> </math> is a plane lamina of the shape of an equilateral triangle. <math><mi>D</mi><mo>,</mo><mi>E</mi></math> are mid points of <math><mi>A</mi><mi>B</mi><mo>,</mo><mi>A</mi><mi>C</mi></math> and <math><mi>G</mi></math> is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through <math><mi>G </mi></math>and (Rotational)

AH→H2H=3a2AG→H3Al=H23MABC=MMADE=M4 ⇒ I G = M a 2 12 - M 4 a 2 2 12 + M 4 a 2 3 2 = 11 16 M a 2 12

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Physics Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Seven

$A B C$ is a plane lamina of the shape of an equilateral triangle. $D, E$ are mid points of $A B, A C$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and (Rotational)

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alok kumar singh | Contributor-Level 10

2 months ago

$\begin{array}{l} A H \to \frac{H}{2} & H = \frac{\sqrt[]{3} a}{2} \\ A G \to \frac{H}{\sqrt[]{3}} & A l = \frac{H}{2 \sqrt[]{3}} \\ M_{A B C} = M & M_{A D E} = \frac{M}{4} \end{array}$

$\Rightarrow I_{G} = \frac{M a^{2}}{12} - [\frac{M}{4} \frac{{[\frac{a}{2}]}^{2}}{12} + \frac{M}{4} {[\frac{a}{2 \sqrt[]{3}}]}^{2}] = (\frac{11}{16}) \frac{{M a}^{2}}{12}$

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$A B C$ is a plane lamina of the shape of an equilateral triangle. $D, E$ are mid points of $A B, A C$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and (Rotational)

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A B C is a plane lamina of the shape of an equilateral triangle. D,E are mid points of AB,AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and (Rotational)

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$A B C$ is a plane lamina of the shape of an equilateral triangle. $D, E$ are mid points of $A B, A C$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and (Rotational)