Change in value of g at a height h above surface of earth is same as at a depth d below surface of e

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7.Gravitation

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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 ?

A

$d = \frac{h}{2}$

B

$d = \frac{3h}{2}$

C

$d = 2h$

D

$d = h$

Solution

$(\Delta \mathrm{g})_{\mathrm{in}}=(\Delta \mathrm{g})_{\mathrm{out}}$

$\left(\frac{\mathrm{d}}{\mathrm{R}}\right) \mathrm{g}=\left(\frac{2 \mathrm{h}}{\mathrm{R}}\right) \mathrm{g}$

$\boxed{{\text{d}} = 2{\text{h}}}$

Standard 11

Physics

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