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Question

Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100kg and they are 100m apart. They are initially at rest relative to one another. How long will it be before the gravitational attraction brings them 1cm closer together?

A
2.52 days
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B
1.41 days
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C
0.70 days
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D
1.41s
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Solution

The correct option is B 1.41 days
a1= acceleration of first
=Gm1m2r2×1m1=Gm2r2=6.67×1011×100(100)2
=6.67×1013 ms1
a2= acceleration of second
=Gm1r2=6.67×1011×100(100)2=6.67×1013 ms1
Net acceleration of approach a=a1+a2=2×6.67×1013 ms1Now, s=12at2
1×102=12×6.67×1013×2×t2Solving, we get t=1.41 days.

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