The change in the value of g at a height ‘ h ’ above the surface of the earth is the same as at a depth ‘ d ’ below the surface of earth. When both ‘ - Physics MCQ AIEEE 2026 | ExamTest.live

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The change in the value of g at a height ‘ h ’ above the surface of the earth is the same as at a depth ‘ d ’ below the surface of earth. When both ‘ d ’ and ‘ h ’ are much smaller than the radius of earth, then which one of the following is correct?

Solution & Step-by-step Explanation

For small h (h ≪ R): g_{h} = g (1 - \frac{2 h}{R}) .For depth d : g_{d} = g (1 - \frac{d}{R}) .If g_{h} = g_{d} : 1 - \frac{2 h}{R} = 1 - \frac{d}{R} \frac{2 h}{R} = \frac{d}{R} ⟹ d = 2 h

Try it yourself before checking the explanation above.

The change in the value of g at a height ‘ h ’ above the surface of the earth is the same as at a depth ‘ d ’ below the surface of earth. When both ‘ d ’ and ‘ h ’ are much smaller than the radius of earth, then which one of the following is correct?

h = 2 d

3 h = 2 d

d = 2 h

d = h

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