Four particles of masses 'm', 'm', '2m' and '2m' are placed at the four corners of a square of side a as shown in diagram The (x, y) coordinates of the centre of mass are

(a, \frac{a}{3})

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(\frac{a}{2}, \frac{2 a}{3})

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(\frac{a}{2}, 2 a)

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(\frac{a}{2}, a)

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Solution

The correct option is B $(\frac{a}{2}, \frac{2 a}{3})$

The (x, y) co-ordinates of the centre of mass are
$x = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3} + m_{4} x_{4}}{m_{1} + m_{2} + m_{3} + m_{4}}$
and $y = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3} + m_{4} y_{4}}{m_{1} + m_{2} + m_{3} + m_{4}}$
It is easy to show that $x = \frac{a}{2}$ and $y = \frac{2 a}{3}$ , which is choice (c).

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The correct option is B (a2,2a3) The (x, y) co-ordinates of the centre of mass are x=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4 and y=m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4 It is easy to show that x=a2 and y=2a3, which is choice (c).