Three identical spheres each of mass M are pl | vedclass

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(A) Let the positions of the three spheres be $(0, 0)$,$(3, 0)$,and $(0, 3)$ in meters.The mass of each sphere is $M$.The position vector of the centr

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$2$

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(A) Let the positions of the three spheres be $(0, 0)$,$(3, 0)$,and $(0, 3)$ in meters.The mass of each sphere is $M$.The position vector of the centre of mass $\overrightarrow{r}_{	ext{com}}$ is given by:$\overrightarrow{r}_{	ext{com}} = \frac{M(0\hat{i} + 0\hat{j}) + M(3\hat{i} + 0\hat{j}) + M(0\hat{i} + 3\hat{j})}{M + M + M}$$\overrightarrow{r}_{	ext{com}} = \frac{M(3\hat{i} + 3\hat{j})}{3M} = \frac{3\hat{i} + 3\hat{j}}{3} = \hat{i} + \hat{j}$The magnitude of the position vector is:$|\overrightarrow{r}_{	ext{com}}| = \sqrt{1^2 + 1^2} = \sqrt{2}$Given that the magnitude is $\sqrt{x}$,we have $\sqrt{x} = \sqrt{2}$,which implies $x = 2$.

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