Question

By symmetry how can we say that x_cm=0 or y_cm=0 in centre of mass

Answer 1

Dear Student

$$\begin{gathered} centreofmassofsystemis \\ {R}_{cm}=\frac{m1r1+m2r2}{m1+m2} \\ atthecenterr1=r2=0 \\ then \\ {x}_{cm}=\frac{m1x1+m2x2}{m1+m2}=\frac{m1\times 0+m2\times 0}{m1+m2}=0 \\ {y}_{cm}=\frac{m1y1+m2y2}{m1+m2}=\frac{m1\times 0+m2\times 0}{m1+m2}=0 \end{gathered}$$

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