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Question 30741
JEE Physics · Hard

Gravitation: g at Combined Height+Depth MCQ

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g at Combined Height+DepthHardQuestion 30741

Question

g at height h = R/2 above surface vs g at depth d = R/2 below surface. Ratio g_h/g_d is:
  1. A
    4/9
    Correct
  2. B
    9/4
  3. C
    4/3
  4. D
    2/3

Correct answer

4/9

Explanation

g_h = g/(1+h/R)² = g/(3/2)² = 4g/9. g_d = g(1−d/R) = g(1/2) = g/2. Ratio = (4g/9)/(g/2) = 8/9. Hmm: g_h = g×R²/(R+R/2)² = g×R²/(3R/2)² = g×4/9. g_d = g(1−R/2R) = g/2. Ratio = (4g/9)/(g/2) = 8/9.

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