Two spherical bodies of masses m and 5m and radii R and 2R respectively, 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, the distance covered by smaller sphere just before collision is

Options

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

Answer

C

Explanation

`x_(1)+x_(2)=9R, (x_(1))/(x_(2)) =(5M)/(M) = 5`
`x_(1)=5x_(2)`
`rArr x_(1)+(x_(1))/(5) = 9R rArr (6x_(1))/(5) =9R`
`x_(1)=7.5R`