Two spherical bodies of mass M and 5 M and radii R and 2 R 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, then the distance covered by by the smaller body before collision is

Options

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

Answer

C

Explanation

Their centre of mass will remain stationary due to the absence of any external force. Hence if the displacement of the smaller and the larger body are `x_(1)` and `x_(2)` respectively,
`Mx_(1)= 5Mx_(2) or, x_(2)= (x_(1))/(5)`
Since at the time of collision the distance between their centres = R +2R , so, net path traversed by the spheres,
`x_(1)+x_(2)=12R-3R=9R`
`:. x_(1)+(x_(1))/(5)=9R or, (6)/(5)x_(1)=9R or, x_(1)=7.5 R`