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?

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Since there is no external force acting on the system of two masses M &5M ,thus COM will remain unaltered.COM will be0.m +5m.12R\6m=10RThus COM is at distance 10R which remain unchanged before and after collision .At collision centre of spherical mass will be 3R apart from each other .Now let the collision takes place at distance x from the origin After collisionmx + 5m(x+3R)\6m=10R6x + 15R=60R6x= 45Rx= 7.5R