Two particles, each of mass m, are initially at rest very far apart. obtain an expression for their relative speed of approach at any instant as a function of their separation distance d if the only interaction is their gravitational attraction to each other. express your answer in terms of some or all of the variables m, d, and gravitational constant g.

Explanation:

Consider two particles are initially at rest.

Therefore,

the kinetic energy of the particles is zero.

That initial K.E. = 0

The relative velocity with which both the particles are approaching each other is Δv and their reduced masses are

now, since both the masses have mass m

therefore,

= m/2

The final K.E. of the particles is

Distance between two particles is d and the gravitational potential energy between them is given by

By law of conservation of energy we have

Now plugging the values we get

This the required relation between G,m and d

3.2x10^7