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  • The triangular plate  is shown in the figure. <img alt="" src="https://cdn.entrance360.com/med

The triangular plate A B C is shown in the figure.

Its mass is ' 1 \mathrm{~kg} ' and its equal sides are given ass ' 1 \mathrm{~m} '. If the angle A is \frac{\pi}{3} then its moment of inertia about an axis passing through A and perpendicular to the plane of plate will be ____

Option: 1

\frac{1}{12} \mathrm{~kg}-\mathrm{m}^2


Option: 2

\frac{5}{12} \mathrm{~kg}-\mathrm{m}^2


Option: 3

\frac{7}{12} \mathrm{~kg}-\mathrm{m}^2


Option: 4

\frac{11}{12} \mathrm{~kg}-\mathrm{m}^2


Answers (1)

best_answer

Using the technique of integration, its moment of inertia about
\begin{aligned} & I=\frac{1}{2} M a^2\left(1-\frac{2}{3} \sin ^2 \frac{\theta}{2}\right) \\ & I=\frac{1}{2} \times 1 \times 1^2\left(1-\frac{2}{3} \sin ^2 \frac{\pi}{6}\right) \\ & I=\frac{1}{2}\left[1-\frac{2}{3} \times \frac{1}{4}\right] \\ & I=\frac{1}{2}\left[1-\frac{1}{6}\right]=\frac{1}{2} \times \frac{5}{6}=\frac{5}{12} \mathrm{~kg}-\mathrm{m}^2 \end{aligned}

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Divya Prakash Singh

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