Two spherical bodies of mass M and 5M & radii R & 2R respectively 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 smallar body just 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`