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Question

Two small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released, assuming that only mutual gravitational forces are acting find the speeds of the particles when the separation decreases to 0.5 m.

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Solution

The linear momentum of 2 bodies is 0 intially. since gravitational force is internal, final momentum is also zero.
So, (10kg)v1=(20kg)v2
orv1=2v2
Since P.E.is conserved,
Initial P.E. =6.67×1011×10×201=13.34×109J
When separation is 0.5 m
13.34×109+0=13.34×10612+(12)×10v21+(12)×20v2213.34×109=26.68×109+5v21+10v2213.34×109=26.68×109+30v22v22=13.34×10930=4.44×1010v2=2.1×105m/sSo,v1=4.2×105m/s


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