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

Options

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

Answer

C

Explanation

Distance between its centres = 12R
Distance between its centre during collision = 3R
Total distance covered by both bodies = `12R-3R=9R`
Suppose distance of body of mass M from centre of mass of both the bodies is x.
Hence distance from body by mass `2M=9R-x`
Internal forces acting between both spheres and hence the centre of mass is constant
`therefore Mx=5M(9R-x)`
`therefore Mx=45MR-5Mx`
`therefore x=45R-5x`
`therefore 6x=45R`
`therefore x=(45)/(6)R`
`therefore x=7.5R`