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Given below are two statements.
Statement I: Acceleration due to the earth's gravity decreases as you go up or down from the earth's surface.
Statement II: Acceleration due to the earth's gravity is the same at a height h and a depth d from the earth's surface, if h=d.

Asked in JEE Main 24th Jan 2nd Shift 2023 · Equal g at a height and a depth

Answer: (1) Statement I is correct but Statement II is incorrect.

Step-by-step solution

Going up, gₕ=g(1+h/R)⁻², and going down, g_d=g(1-d/R); both are smaller than g, so Statement I is correct.

For small distances gₕ≈ g(1-(2h)/R) while g_d=g(1-d/R).

With h=d the height value drops twice as fast, so the two are not equal and Statement II is incorrect.

Why the other options are wrong

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