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

Options

A. `2.5 R`
B. `4.5R`
C. `7.5R`
D. `1.5R`

Answer

C

Explanation

Initial position

Just before collision
For this system, position fo centre of mass remains same
`[:. Vec(F)_("system") = 0]`
`(M(0) + 5M(12R))/(M + 5M) = (M(d) + 5M (d + 3R))/(M + 5M) rArr d = 7.5 R`