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

Answer

C

Explanation

Both the bodies due to gravitational force only hence no external force on the system of the bodies it means the centre of mass of the bodies will remain stationary.

Let the distance moved by spherical body of mass `M` is `x_(1)` and by spherical body of `5M` `x_(2)`
So, `(M)(x_(1))=(5M)(x_(2))`
or `x_(1)=5x_(2)`
and for touching `x_(1)+x_(2)=9R`
so, `x_(1)=7.5R`