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What is the correct integral for finding the the x-component of the center of mass of an isosceles triangle of length L, and base B, as shown in the figure below? y dx thickness=T B Xcom = L² Só xdx Xcom = L² S x²dx В L x²dx Xcom L² O xcom = xdx L² Xcom = 6 x²dx %3D (x)M

What is the correct integral for finding the the x-component of the center of mass of an isosceles triangle of length L, and base B, as shown in the figure below? y dx thickness=T B Xcom = L² Só xdx Xcom = L² S x²dx В L x²dx Xcom L² O xcom = xdx L² Xcom = 6 x²dx %3D (x)M

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**Educational Content: Finding the X-Component of the Center of Mass for an Isosceles Triangle** **Problem Statement:** What is the correct integral for finding the x-component of the center of mass of an isosceles triangle of length \( L \) and base \( B \), as shown in the figure below? **Diagram Explanation:** The diagram displays a red isosceles triangle with its base along the x-axis and its vertex on the y-axis. The triangle has: - Length \( L \) along the x-axis. - Base \( B \) perpendicular to the x-axis. - A variable width \( w(x) \) at a distance \( x \) from the vertex. - A small section of thickness \( dx \) is highlighted in blue to indicate an element of integration over the triangle's length \( L \). The thickness of the entire triangle is labeled \( T \). **Multiple Choice Options:** 1. \( x_{\text{com}} = \frac{B}{L^2} \int_0^L x \, dx \) (Correct answer) 2. \( x_{\text{com}} = \frac{2}{L^2} \int_0^L x^2 \, dx \) 3. \( x_{\text{com}} = \frac{1}{L^2} \int_0^B x^2 \, dx \) 4. \( x_{\text{com}} = \frac{2}{L} \int_0^L x \, dx \) 5. \( x_{\text{com}} = \frac{1}{L^2} \int_0^L x^2 \, dx \)
Transcribed Image Text:**Educational Content: Finding the X-Component of the Center of Mass for an Isosceles Triangle** **Problem Statement:** What is the correct integral for finding the x-component of the center of mass of an isosceles triangle of length \( L \) and base \( B \), as shown in the figure below? **Diagram Explanation:** The diagram displays a red isosceles triangle with its base along the x-axis and its vertex on the y-axis. The triangle has: - Length \( L \) along the x-axis. - Base \( B \) perpendicular to the x-axis. - A variable width \( w(x) \) at a distance \( x \) from the vertex. - A small section of thickness \( dx \) is highlighted in blue to indicate an element of integration over the triangle's length \( L \). The thickness of the entire triangle is labeled \( T \). **Multiple Choice Options:** 1. \( x_{\text{com}} = \frac{B}{L^2} \int_0^L x \, dx \) (Correct answer) 2. \( x_{\text{com}} = \frac{2}{L^2} \int_0^L x^2 \, dx \) 3. \( x_{\text{com}} = \frac{1}{L^2} \int_0^B x^2 \, dx \) 4. \( x_{\text{com}} = \frac{2}{L} \int_0^L x \, dx \) 5. \( x_{\text{com}} = \frac{1}{L^2} \int_0^L x^2 \, dx \)
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