Two masses $$m1$$ and $$m2$$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is

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Infinity Learn · Accepted Answer

As there is no external force acting on the system, linear momentum of the system is $$conserved.0=m1V1$$→$$+m2V2$$→ magnitude $$V2=m1V1m2---1the$$ relative velocity of approach is $$V2$$→$$-V1$$→$$=V2+V1=m1+m2m2V1----2Applying$$ conservation of mechanical energy for the $$system0=-Gm1m2d+12m1V12+12m2V22$$ substituting (1) in the above we get $$V1=2Gm22m1+m2dSubstitute$$ $$V1$$ in (2) we getrelative velocity of approach $$=2Gm1+m2d$$

Two masses m₁ and m₂ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is

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Two masses m1 and m2 are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is

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Two masses m₁ and m₂ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is