Two uniform plates of the same thickness and | vedclass

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(C) Let the dimensions of the plates be as shown in the figure. Let the base of the triangle and the width of the rectangle be $a$,the height of the t

Vedclass · Accepted Answer

$3: 4$

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(C) Let the dimensions of the plates be as shown in the figure. Let the base of the triangle and the width of the rectangle be $a$,the height of the triangle be $h$,and the height of the rectangle be $b$.Given that the area of the triangle equals the area of the rectangle:$\frac{1}{2} a h = a b \Rightarrow \frac{h}{2} = b \Rightarrow \frac{b}{h} = \frac{1}{2}$.Let the origin be at the mid-point of the common side. The centre of mass of the triangular part is at a distance $y_1 = \frac{h}{3}$ above the origin.The centre of mass of the rectangular part is at a distance $y_2 = -\frac{b}{2}$ below the origin.For the composite body,the centre of mass is at the origin,so $Y_{CM} = 0$.Using the formula $Y_{CM} = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2} = 0$,we get:$m_1 y_1 + m_2 y_2 = 0 \Rightarrow m_1 \left(\frac{h}{3}ight) + m_2 \left(-\frac{b}{2}ight) = 0$.$\Rightarrow m_1 \left(\frac{h}{3}ight) = m_2 \left(\frac{b}{2}ight)$.$\Rightarrow \frac{m_1}{m_2} = \frac{3b}{2h} = \frac{3}{2} 	imes \frac{b}{h} = \frac{3}{2} 	imes \frac{1}{2} = \frac{3}{4}$.Therefore,the ratio of the masses $m_1 : m_2 = 3 : 4$.

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