Question

What would be the value of acceleration due to gravity at a point 5 km below the earth's surface?
(Take, R_E = 6400 km, g_E = 9.8 ms^-2) [UK PMT 2015]

Moderate

Solution

The value of g at a depth d from the earth's surface,
$g = g_{E} (1 - \frac{d}{R_{E}})$
where, g_E is acceleration due to gravity at the earth's surface and R_E is the radius of earth.
$\Rightarrow g = 9.8 (1 - \frac{5}{6400}) = 9.8 (\frac{6395}{6400}) = 9.79 {ms}^{- 2}$

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