Question

Four particles of mass 5, 3, 2 and 4 kg are at the points (1,6), (-1,5), (2,-3) and (-1,-4) respectively. Find the coordinate of their centre of mass.

• A. $(\frac{2}{7},\frac{23}{4})$
• B. $(\frac{1}{7},\frac{23}{14})$
• C. $(\frac{1}{7},\frac{23}{3})$
• D. $(\frac{2}{7},\frac{11}{4})$

Answer 1

The correct option is B $(\frac{1}{7},\frac{23}{14})$

$x_{com}=\frac{5\times 1-3\times 1+2\times 2+4\times -1}{5+3+2+4}=\frac{1}{7}$
$y_{com}=\frac{6\times 5+3\times 5-2\times 3+4\times (-4)}{14}$
$=\frac{30+15-6-16}{14}=\frac{45-22}{14}=\frac{23}{14}$