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Question 30719
JEE Physics · Hard

Gravitation: Zero Gravity Point MCQ

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Zero Gravity PointHardQuestion 30719

Question

Between Earth (mass M) and Moon (mass m, distance d apart), the point where net gravitational field is zero lies at distance x from Earth where:
  1. A
    x = d/(1 + √(M/m))
  2. B
    x = d√M/(√M + √m)
    Correct
  3. C
    x = d×M/(M+m)
  4. D
    x = d/(1 + m/M)

Correct answer

x = d√M/(√M + √m)

Explanation

GM/x² = Gm/(d−x)². Taking square roots: √M/x = √m/(d−x). Cross multiply: (d−x)√M = x√m → d√M = x(√M + √m) → x = d√M/(√M + √m).

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