A system consist of three particles each of mass $m$ located at point $(1, 1), (2, 2)$ and $(3, 3)$ . The coordinates of the centre of the mass are:

(6,6)

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(3,3)

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(1,1)

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(2,2)

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(5,5)

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Solution

The correct option is D (2,2)

$x_{c m} = \frac{m_{1} X_{1} + m_{2} X_{2} + m_{3} X_{3}}{m_{1} + m_{2} + m_{3}}$
$= \frac{m \times 1 + m \times 2 + m \times 3}{3 m} = 2$
$y_{c m} = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3}}{3 m}$
$y_{c m} = \frac{m \times 1 + m \times 2 + m \times 3}{3 m} = 2$
$∴$ COM are $(2, 2)$

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