Two spherical bodies of mass M and 5M and radii R and 2R 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 smaller body before collision is

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(1) 7.5 R. No external force acts, so the centre of mass stays put and the displacements satisfy Mx₁=5Mx₂, giving x₁=5x₂. They touch when their centres are R+2R=3R apart. So the separation closes by 12R-3R=9R, which means x₁+x₂=9R. Substituting x₁=5x₂: 6x₂=9R, so x₂=1.5R. The smaller body therefore covers x₁=5×1.5R=7.5R.

Two spherical bodies of mass M and 5M and radii R and 2R 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 smaller body before collision is

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