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. 4.5 R
C. 7.5 R
D. 1.5 R

Answer

C

Explanation

Centre of mass remains at same place.

Let P is the point where centre of mass of whole system lies and must be closer to bigger object.
Let `x_(1)` and `x_(2)` be the distances travelled by two bodies.
`x_(1) + x_(2) = 9R` ...(i)
`Mx_(1) = 5M(x_(2))` ...(ii)
From equations (i) and (ii)
`6x_(2) = 9R`
Distance travelled by bigger body, `x_(2) = (3)/(2)R = 1.5 R`
Distance travelled by smaller body, `x_(1) = 7.5 R`