Question

Two charged body of mass m and 2m separated by distance d at what point they collid

Answer 1

solution:

He conservation law of momentum gives you  

v2v1=−m1m2v2v1=−m1m2

Substitute this into v1- v2 giving v1(m1+m2)/m2.

We can also apply momentum conservation again to the kinetic energy ratio  

k1k2=m2m1k1k2=m2m1.  

That's nice, and it eliminates an energy :

k1+k2 = k1(m1+m2)/m2

now,  we set that to Gm1m2/r

But the pesky k1 still needs to be removed, so expand it giving

v1^2 = 2Gm2^2/(m1+m2)r

The easy way to finish off is square the relative velocity

Vrel^2 = v1^2 * ((m1+m2)/m2)^2 and just plug in v1^2