Question

two charged particles of equal mass +9 and -9 are placed a distance r apart from each other. What is the time taken for them to collide

Answer 1

\[Force = mass * acceleration\] The force in this case is the sum of that due to gravitational "attraction" and that due to attraction between opposite electrical charges. For your particles, assuming them to be points, both are inversely proportional to the square of the distance.

As an aside, gravity is more accurately described as a curvature of spacetime, see general relativity. However, for this purpose, the Newtonian description is sufficient.

To solve, you will need to call on Newton's law of universal gravitation and Coulomb's law. Both have the same form:
\[F=k(n1 * n2)/r^2\] n1 and n2 are properties of your particles, mass or charge. k is the relevant constant, gravitational or Coloumb's, and r is the distance between your particles. This force acts on both particles. By symmetry, the particles will collide after they travel a distance of r/2, so you calculate your acceleration and use that to determine the time taken to travel this distance.

Answer 2

Oh, one other assumption: Both particles are initially at rest relative to one another.