Two spherical bodies of masses M and 5 M and radius R and 2R respectively 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 covered by the smaller body just before collision is

Options

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

Answer

C

Explanation

Distance between the centres of spheres = 12 R
`therefore` Distance between their surfaces `=12R-(2R+R)=9R`
Since there is no external force, hence centre of mass must remain unchanged and hence
`rArr m_(1)r_(1)=m_(2)r_(2) rArr Mx=5M(9R-x)`, where x = distance covered by smaller body.
`rArr x=7.5R`