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

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

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

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

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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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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,a3)(a2,2a3) (a2,2a) (a2,a)

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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

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

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