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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?

1. d = 3h/2
2. d = h/2
3. d = h
4. d = 2h

Correct answer: d = 2h

Solution

Decrease in g at small height: dg = 2gh/R; decrease at small depth: dg = gd/R. Equating gives 2h = d, so d = 2h.

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