Three equal masses lie at the corners of an equilateral triangle of side l. find the center of mass.

If two of the masses are at (0, 0) and (L, 0), by symmetry the x-coordinate of the third mass must be L/2, and then by the Pythagorean theorem its y-coordinate must be L(âš3)/2. Thus the position of the third mass is (L/2, L(âš3)/2). Let each mass be m and C be the position of its center of mass. Then C = (1/(3m)) (m(0, 0) + m(L, 0) + m(L/2, L(âš3)/2)). = (1/3) (3L/2, L(âš3)/2). = (L/2, L(âš3)/6). That is, X_c = L/2 and Y_c = L(âš3)/6.

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -