The correct option is D 7.5 R
As the distance between two sphere is 9R. Let before collision small sphere moves x distance and the bigger sphere move (9R−x) distance,
Force of attraction between two sphare due to gravity is given by,
f=GM′mr2
As given, M′=M, m=5M, r=12R
So, F=5GM2(12R)2
Now, acceleration of small sphere will be
asmall=FM=5GM(12R)2
Acceleration of bigger sphere will be
abig=F5M=GM(12R)2
By using Newton's law of motion
x=12asmallt2
x=125GM(12R)2t2
x5=12GM(12R)2t2(1)
(9R−x)=12abigt2
(9R−x)=12GM(12R)2t2(2)
From eq. (1) and eq. (2)
x5=(9R−x)
x=45R−5x
x=7.5R