Question

A uniform square wooden sheet of side a has its centre of mass located at point 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 centre of mass of the L-shaped sheet lies at the point P (in the diagram) when

• A. $\frac{a}{b}=\frac{(\sqrt{5}-1)}{2}$
• B. $\frac{a}{b}=\frac{(\sqrt{5}+1)}{2}$
• C. $\frac{a}{b}=\frac{(\sqrt{3}-1)}{1}$
• D. $\frac{a}{b}=\frac{(\sqrt{3}+1)}{2}$

Answer 1

The correct option is B

$\frac{a}{b}=\frac{(\sqrt{5}+1)}{2}$

Finally com at p

$x_{am}=\frac{A_1{X}_1+A_2{X}_2}{A_1+A_2}(a-b)=\frac{a(a-b\frac{(a-b)}{2})+b(a-b)(a-b+\frac{b}{a})}{a(a-b)+(a-b)b}\therefore {\left(\frac{a}{b}\right)}^2-\left(\frac{a}{b}\right)-1=0\frac{a}{b}=\frac{1+\sqrt{5}}{2}$