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Question

(A) The coordinates of the masses arranged on the circle of radius $R = 1 \ m$ are:$M$ at $(1, 0)$$2M$ at $(0, 1)$$3M$ at $(-1, 0)$$4M$ at $(0, -1)$Th

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$-\frac{1}{5} \hat{i} - \frac{1}{5} \hat{j}$

Vedclass · Answer

(A) The coordinates of the masses arranged on the circle of radius $R = 1 \ m$ are:$M$ at $(1, 0)$$2M$ at $(0, 1)$$3M$ at $(-1, 0)$$4M$ at $(0, -1)$The $x$-coordinate of the center of mass $(X_{cm})$ is given by:$X_{cm} = \frac{M(1) + 2M(0) + 3M(-1) + 4M(0)}{M + 2M + 3M + 4M} = \frac{M - 3M}{10M} = \frac{-2M}{10M} = -\frac{1}{5} \ m$The $y$-coordinate of the center of mass $(Y_{cm})$ is given by:$Y_{cm} = \frac{M(0) + 2M(1) + 3M(0) + 4M(-1)}{M + 2M + 3M + 4M} = \frac{2M - 4M}{10M} = \frac{-2M}{10M} = -\frac{1}{5} \ m$Thus,the position vector of the center of mass is $-\frac{1}{5} \hat{i} - \frac{1}{5} \hat{j}$.

Four masses are arranged along a circle of radius $1 \ m$ as shown in the figure. The center of mass of this system of masses is at

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