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Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1. -4Gm/r
2. -6Gm/r
3. -9Gm/r
4. zero

Correct answer: -9Gm/r

Solution

Field is zero where m/x^2 = 4m/(r-x)^2, giving x = r/3 from mass m (so 2r/3 from 4m). Potential there V = -Gm/(r/3) - G(4m)/(2r/3) = -3Gm/r - 6Gm/r = -9Gm/r.

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