Two spherical bodies of mass ‘M’ and 5M and radii R and 2R 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 before collision is

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7.5 R

1.5R

2.5R

4.5R

answer is A.

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Detailed Solution

The force between the two mass is internal and hence the centre of mass of the system is constant Initial center of mass is Xcm=m1x1+m2x2m1+m2=M0+5M12RM+5M=60R6=10RFinal centre of mass isXcm1=Mx1+5Mx1+3RM+5M∴Xcm=Xcm1substitute Xcm=10R and cross multiply60R=x1+5x1+15R∴x1=7.5R

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