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A uniform square wooden sheet of side a has its center of mass located at point $\mathrm{O}$ as shown in the figure on the left. A square portion of side $b$ of this sheet is cut out to produce and L-shaped sheet as shown in the figure on the right.
The center of mass of the L-shaped sheet lies at the point $\mathrm{P}$ (in the diagram) when
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The center of mass of the L-shaped sheet lies at the point $\mathrm{P}$ (in the diagram) when
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The correct answer is:
$a / b=(\sqrt{5}+1) / 2$
Finaly com at $p$
$\mathrm{X}_{\mathrm{am}}=\frac{\mathrm{A}_{1} \mathrm{X}_{1}+\mathrm{A}_{2} \mathrm{X}_{2}}{\mathrm{~A}_{1}+\mathrm{A}_{2}}$
$(a-b)=\frac{a(a-b) \frac{(a-b)}{2}+b(a-b)(a-b+b / 2)}{a(a-b)+(a-b) b}$
$\begin{array}{l}
\therefore\left(\frac{a}{b}\right)^{2}-\left(\frac{a}{b}\right)-1=0 \\
\frac{a}{b}=\frac{1+\sqrt{5}}{2}
\end{array}$
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