Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Three particles of masses \( 100\text{ g} \), \( 150\text{ g} \), and \( 200\text{ g} \) are placed at the vertices of an equilateral triangle of side \( 0.5\text{ m} \) as shown in the text coordinate system: \( 100\text{ g} \) at \( (0,0) \), \( 150\text{ g} \) at \( (0.5,0) \), and \( 200\text{ g} \) at \( (0.25, 0.25\sqrt{3}) \). What is the distance of the centre of mass from the origin?

1. A
   \( \frac{\sqrt{43}}{18\sqrt{3}}\text{ m} \)
2. B
   \( \frac{\sqrt{13}}{9\sqrt{3}}\text{ m} \)
3. C
   \( \frac{\sqrt{37}}{18}\text{ m} \)
4. D
   \( \frac{\sqrt{37}}{18\sqrt{3}}\text{ m} \)