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
medium
Work, Energy and Power
2015
physics
4.5R
7.5R
1.5R
2.5R
Explanation
To solve this problem, we need to determine the distance covered by the smaller body before the collision.Given:ā¢ Mass of the smaller body =Mā¢ Mass of the larger body =5Mā¢ Radius of the smaller body =R
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When two bodies attract each other due to gravitational force, they will move towards each other and collide when the distance between their surfaces becomes zero.
The initial separation between the surfaces of the two bodies is:
dinitialā=12Rā(R+2R)=9R
Let
s1ā
be the distance covered by the smaller body and
s2ā
be the distance covered by the larger body.
Since the bodies attract each other due to gravitational force, their center of mass remains constant.
The center of mass
xcmā
is given by:
xcmā=M+5MMā 0+5Mā 12Rā=6M60MRā=10R
The center of mass does not move, so the total distance covered by both bodies is