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

1. 4.5 R
2. 7.5 R
3. 1.5 R
4. 2.5 R

Correct answer: 4.5 R

Solution

The center of mass of the system remains stationary as no external force acts on it. The distance moved by the smaller body before collision is determined by the ratio of their masses. The smaller body will move a distance of (5M / (M + 5M)) × 12R = 4.5R.

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