Four point masses are placed at the corners of a square of side $2 m$ as shown in figure. Find the centre of mass of the system w.r.t the centre of square

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Solution

Given,

$m_{a} = 4 k g, m_{b} = 1 k g, m_{c} = 3 k g a n d m_{4} = 2 k g$

Position $a (- 1, 1), b (1, 1), c (- 1, - 1)$ and $d (1, - 1)$

$X = \frac{m_{a} x_{a} + m_{b} x_{b} + m_{c} x_{c} + m_{d} x_{d}}{m_{a} + m_{b} + m_{c} + m_{d}}$

$Y = \frac{m_{a} y_{a} + m_{b} y_{b} + m_{c} y_{c} + m_{d} y_{d}}{m_{a} + m_{b} + m_{c} + m_{d}}$

$X = \frac{4 \times (- 1) + 1 \times 1 + 3 \times (- 1) + 2 \times 1}{4 + 1 + 3 + 2} = - 0.4 m$

$Y = \frac{4 \times 1 + 1 \times 1 + 3 \times (- 1) + 2 \times (- 1)}{4 + 1 + 3 + 2} = 0 m$

Hence, distance from center of mass from center of square is $0.4 m$ left

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Four point masses are placed at the corners of a square of side 2m as shown in figure. Find the centre of mass of the system w.r.t the centre of square

Four point masses are placed at the corners of a square of side $2 m$ as shown in figure. Find the centre of mass of the system w.r.t the centre of square