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(A) To find the $y$-coordinate of the centre of mass $(Y_{CM})$,we use the formula: $Y_{CM} = \frac{\sum m_i y_i}{\sum m_i}$.The components and their

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$\frac{a}{10}$

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(A) To find the $y$-coordinate of the centre of mass $(Y_{CM})$,we use the formula: $Y_{CM} = \frac{\sum m_i y_i}{\sum m_i}$.The components and their respective masses $(m_i)$ and $y$-coordinates $(y_i)$ are:$1$. Outer circle: $m_1 = 6m$,$y_1 = 0$$2$. Left inner circle: $m_2 = m$,$y_2 = a$$3$. Right inner circle: $m_3 = m$,$y_3 = a$$4$. Vertical line: $m_4 = m$,$y_4 = 0$$5$. Horizontal line: $m_5 = m$,$y_5 = -a$Total mass $M = 6m + m + m + m + m = 10m$.Calculating $Y_{CM}$:$Y_{CM} = \frac{(6m 	imes 0) + (m 	imes a) + (m 	imes a) + (m 	imes 0) + (m 	imes -a)}{10m}$$Y_{CM} = \frac{0 + ma + ma + 0 - ma}{10m}$$Y_{CM} = \frac{ma}{10m} = \frac{a}{10}$.

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