Question

If the change in value of g at height h above the surface of the earth is the same as at a depth d below the surface of the earth, when both d and h are much smaller than the radius of the Earth, then which one of the following is true?

Options

• d = h

• d = 2h

• d = `"h"/2`

• d = `(3"h")/2`

Answer 1

d = 2h

Explanation:

`"g"_"h" = "g"(1 - "2h")/"R"` and

`"g"_"d" = "g"(1 - "d"/"R")` But g_h = g_d

`therefore 1 - (2"h")/"R" = 1 - "d"/"R"`

∴ d = 2h