Four particles of masses m, 2m, 3m, 4m are pl | vedclass

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(D) Let the positions of the particles be:$m$ at $(0, 0)$$2m$ at $(a, 0)$$3m$ at $(a, a)$$4m$ at $(0, a)$The $x$-coordinate of the center of mass is g

Vedclass · Accepted Answer

$\left( \frac{a}{2}, \frac{7}{10}a \right)$

Vedclass · Answer

(D) Let the positions of the particles be:$m$ at $(0, 0)$$2m$ at $(a, 0)$$3m$ at $(a, a)$$4m$ at $(0, a)$The $x$-coordinate of the center of mass is given by:$X_{CM} = \frac{m(0) + 2m(a) + 3m(a) + 4m(0)}{m + 2m + 3m + 4m} = \frac{5ma}{10m} = \frac{a}{2}$The $y$-coordinate of the center of mass is given by:$Y_{CM} = \frac{m(0) + 2m(0) + 3m(a) + 4m(a)}{m + 2m + 3m + 4m} = \frac{7ma}{10m} = \frac{7}{10}a$Thus,the coordinates of the center of mass are $\left( \frac{a}{2}, \frac{7}{10}a \right)$.

Four particles of masses $m, 2m, 3m, 4m$ are placed at the corners of a square of side $a$ as shown in the figure. Find the coordinates of the center of mass.

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