The figure shows a metallic plate of uniform density. The value of $\ell$ in terms of $L$ and $b$ so

Question

The figure shows a metallic plate of uniform density. The value of $\ell$ in terms of $L$ and $b$ so that the center of mass of system lies at the interface of the triangular and rectangular portion.

Professor PC Thomas Classes · Answer

From the figure, $A_1=\frac{1}{2} b L ; y_1=\frac{L}{3}$ and $A_2=b \ell ; y_2=\frac{\ell}{2}$ If the center of mass of the system lies at the interface, then \ $ \begin{aligned} & A_1 y_1=A_2 y_2 \ & \left(\frac{1}{2} b Light) \frac{L}{3}=(b l) \frac{l}{2} \end{aligned} $ or $ \ell=\frac{L}{\sqrt{3}} $