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Two bodies of masses m1 and m2 are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is

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a

2Gm1+m2r1/2

b

2Grm1+m221/2

c

r2Gm1m21/2

d

2Grm1m21/2

answer is A.

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Detailed Solution

If v be the relative velocity of approach , then we can write , μvdvdr = -Gm1m2r where μ = m1m2m1+m2= Reduced mass. ⇒∫0vv dv = -G(m1+m2)∫∞r1rdr ⇒v=2G(m1+m2)r Hence the correct choice is (1).
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Two bodies of masses m1 and m2 are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is