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Q.

Two spherical bodies of mass M and 5 M and radii R and 2 R are 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

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a

7.5 R

b

1.5 R

c

2.5 R

d

4.5 R

answer is A.

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Detailed Solution

Position of center of mass of the system from m x1=5mx12R6m=10Rwhen they meet they touch each other and separation between them becomes 3R and center of mass from m x2=5mx3R6m=2.5Ras center of mass is stationary due to absence of any external force so m  moves by a distance  of  x1-x2=7.5R
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Two spherical bodies of mass M and 5 M and radii R and 2 R are 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