Question

Find the centre of mass of three particles at vertices of an equilateral triangle.the masses of the part

Answer 1

Assuming the masses of particles are same and equal to m and the side of the triangle to be a.

If we put one vertice in the center of coordinate axes, coordinate of the vertices becomes (0,0), (a,0), $(\frac{a}{2},\frac{\sqrt{3}a}{2})$

so the x coordinate of center of mass is,

$x_{cm}= \frac{0+a+\frac{a}{2}}{3}$
$x_{cm}=\frac{a}{2}$

and the y coordinate is,

$y_{cm}=\frac{0+0+\frac{\sqrt(3)a}{2}}{3}$
$y_{cm}=\frac{\sqrt(3)a}{6}$