Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :-

Initial distance between their centers$=12R$

At time of collision the distance between their centers $=3R$ 

So total distance travelled by both $=12R-3R=9R$ 

Since the bodies move under mutual forces, center of mass will remain stationary so

$\begin{array}{r}{\mathrm{m}}_1{\mathrm{x}}_1={\mathrm{m}}_2{\mathrm{x}}_2\\ \mathrm{mx}=5\mathrm{m}(9\mathrm{R}-\mathrm{x})\\ \mathrm{x}=45\mathrm{R}-5\mathrm{x}\\ 6\mathrm{x}=45\mathrm{R}\\ \mathrm{x}=\frac{45\mathrm{R}}{6}\\ \mathrm{x}=7.5\mathrm{R}\end{array}$