9-13 할리데이 11판 솔루션 일반물리학

$$\put\begin{cases} A:\text{3d x 3d Box}\\ B:\text{2d x 2d Box}\\ C:\text{A-B Box} \end{cases}$$ $$\begin{cases} 6d&=6.0\ut{m}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{cases} x_{\com A} &=0\\ x_{\com B}&=2d\\ \end{cases}$$ $$\vec r_{\com} = \frac{\Sigma m\vec r}{M}= \frac{\Sigma V\vec r}{V_s},$$ $$\begin{aligned} x_{\com A}&= \frac{\Sigma V\vec r}{V_A}\\ &=\frac{V_Bx_{\com B}+V_Cx_{\com C}}{V_A}\\ \end{aligned}$$ $$\begin{aligned} x_{\com C}&=\frac{V_Ax_{\com A}-V_Bx_{\com B}}{V_C}\\ &=\frac{h(6d)^2x_{\com A}-h(2d)^2x_{\com B}}{h(6d)^2-h(2d)^2}\\ &=\frac{6^2\cdot0-2^2\cdot(2d)}{6^2-2^2}\\ &=-\frac{d}{4}\\ &=-2.0\ut{m}\\ \end{aligned}$$ $$\ab{b}$$ $$\text{Symmetrical about }y,$$ $$y_{\com C}=0$$