Applying momentum conservation.
0=2mv1−3mv2
⇒v2=2v13............(i)
From energy conservation,
ki+Ui=kf+Ur
0+(−G3m2R2m)=122mv21+12(3m)v22
+(−32G(3m)R)(2m).........(ii)
Solving eqn.(i) & (ii) get,
v1=√18Gm5R
(A) COM will be fixed and assume that x is displacement of cosmic particle
Scm=m1s1+m2s2m1+m2⇒x=1.2R
(B)Fnet=0⇒a=0
(D)Wgr=U↓
⇒Wgr=(−G(3m)2R)2m−(32G(3m2)R)2m=6Gm2R