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 = ${\displaystyle \frac{\text{h}}{2}}$

• d = ${\displaystyle \frac{3\text{h}}{2}}$

Answer 1

d = 2h

Explanation:

${\displaystyle {\text{g}}_{\text{h}}=\text{g}\frac{1-\text{2h}}{\text{R}}}$ and

${\displaystyle {\text{g}}_{\text{d}}=\text{g}(1-\frac{\text{d}}{\text{R}})}$ But g_h = g_d

${\displaystyle \therefore 1-\frac{2\text{h}}{\text{R}}=1-\frac{\text{d}}{\text{R}}}$

∴ d = 2h