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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
$d = \frac{{3h}}{2}$
B
$d = \frac{h}{2}$
C
$d = h$
D
$d =2\, h$
Solution
Variation of $\mathrm{g}$ with altitude is,
$\mathrm{g}_{\mathrm{h}}=\mathrm{g}\left[1-\frac{2 \mathrm{h}}{\mathrm{R}}\right]$
variation of $\mathrm{g}$ with depth is,
$\mathrm{g}_{\mathrm{d}}=\mathrm{g}\left[1-\frac{\mathrm{d}}{\mathrm{R}}\right]$
Equating $\mathrm{g}_{\mathrm{h}}$ and $\mathrm{g}_{\mathrm{d}},$ we get $\mathrm{d}=2 \mathrm{h}$
Standard 11
Physics
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