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zorro
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Homework Statement
2 particles of masses M and m are initially at rest and infinitely separated. When they move towards each other due to gravitational attraction, what is their relative velocity at any instant?
Homework Equations
The Attempt at a Solution
The problem may be treated in centre of mass system co-ordinates. Therefore,
reduced mass R= Mm/(M+m)
Kinetic energy = 0.5RVrel2
Work done in moving masses from infinite distance to a separation distance d can be found by integration.
W.D. = -GMm/d
Now by using Work-Energy theorem,
K.E.f - K.E.i = W.D
0.5RVrel2 - 0 = -GMm/d
Vrel = [-2G(M+m)/d]^1/2
but the answer is
[2G(M+m)/d]^1/2
Where am I wrong?