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 ?
A.
$$d = \frac{{3h}}{2}$$
B.
$$d = \frac{{h}}{2}$$
C.
$$d = h$$
D.
$$d = 2h$$
Answer :
$$d = 2h$$
Solution :
Variation of $$g$$ with altitude is, $${g_h} = g\left[ {1 - \frac{{2h}}{R}} \right];$$
variation of $$g$$ with depth is, $${g_d} = g\left[ {1 - \frac{d}{R}} \right]$$
Equating $${g_h}$$ and $${g_d},$$ we get $$d=2h$$
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