Two bodies of masses  M each are kept at a distance D in free space where there is no external gravity force. How much time will it take for the bodies to collide each other ?

How come? Does it mean that they will never collide? I don't have the answer.

ya they will never collide. they are just kept in space . there is no external force given to them so that they will move towars each other

square root of m/d³

look by symettry i can say that they collide at the midpt.....proof: there is no shift in cm of the system(ext F=0)

so evn towards the end the centre of mass will remain at the midpt only...assume the midpt to be the origine....and the two particles at (D/2,0) and (-D/2,0) respctly....the force eqn for particle at origine will be sumwat like this....

- mVdV/dx = Gm²/(2x)²....if it is at a dist. 2x frm the other mass...it will be at a dist of x frm origine...

integrate it frm D to 'x' and frm 0 to V....write V as dx/dt and u know wat 2 do(integrate frm 0 to 'T'..and frm D to 0) and T is ur time taken....jus. giving the brief mtd...

hope it helped

rate if useful......