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

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

Grade:12th pass

1 Answers

Soumya Ranjan Mohanty
117 Points
6 years ago
Dear student,
The center of mass of the 2 body system will not be changed because there is no external force acting on the system.
Let mass M be initially at origin. Centre of mass will be
X=(0*M + 5M*12R)/(5M+M)
=>X=10R
so center of mass is at distance 10R and it reamins unchanged before and after collision happens.
During collision, centre of masses will be 3R apart. If collision takes place at dist x from origin,
after colllision x= (mx+5m(x+3R)}/6m =10R
=>6x+15R=60R=>x=7.5R [Ans]
Regards,
Thank you,
Soumya Ranjan Mohanty.

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