Question

If the change in the value of g at the height h above the surface of the earth is the same as at a depth x below it, then ______.

(both x and h being much smaller than the radius of the earth)

Options

• x = h

• x = 2h

• x = h/2

• x = h²

Answer 1

If the change in the value of g at the height h above the surface of the earth is the same as at a depth x below it, then x = 2h.

Explanation:

The value of g at the height h from the surface of earth

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

The value of g at depth x below the surface of earth

g' = g`(1-x/"R")`

These two are given equal, hence

`(1-(2"h")/"R")=(1-x/"R")`

On solving, we get x = 2h