The gravitational force acting on both the masses is the same. F1=F2 ma1=ma2 ⇒
9M
95M
=
5M
M
=5 ⇒
9M
95M
=
1
5
.......(i) Let t be the time taken for the two masses to collide and x5M,xM be the distance travelled by the mass 5M and M respectively. For mass 5M u=0, S=ut+
1
2
at2 ∴x5M=
1
2
a5Mt2 ....(ii) For mass M u=0,s=xM,t=t,a=aM ∴s=ut+
1
2
at2 ⇒xM=
1
2
aMt2 … (iii) Dividing (ii) by (iii)
x5M
xM
=
1
2
a5Mt2
1
2
aMt2
=
a5M
aM
=
1
5
[From (i)] ∴5x5M=xM ....(iv) From the figure it is clear that x5M+xM=9R ....(v) Where O is the point where the two spheres collide. From (iv) and (v)