A uniform lamina ABCDE is made from a square ABDE and an equilateral triangle BCD. Find the x coordinate of centre of mass of the lamina

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7.4a

0.74a

0.5a

$a + \frac{a}{2 \sqrt{3}}$

answer is A.

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Detailed Solution

$\begin{array}{ll} x_{cm} = \frac{A_{1} x_{1} + A_{2} x_{2}}{A_{1} + A_{2}} = 0 .74 a \\ h e r e, A_{1} = a^{2}, x_{1} = \frac{a}{2} \\ A_{2} = \frac{\sqrt{3} a^{2}}{4}, x_{2} = a + \frac{a}{2 \sqrt{3}} \end{array}$

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