Question

Which of the following statement is correct'? (Take, earth as a sphere of uniform density)

Moderate

Solution

Acceleration due to gravity at altitude h,
$g_{h} = \frac{g}{(1 + h / R)^{2}} \approx g (1 - \frac{2 h}{\dot{R}})$ …(i)
At depth d,
$g_{d} = g (1 - \frac{d}{R})$ …(ii)
In both Eqs. (i) and (ii), if h and d increases, g decreases.
At latitude $ϕ, g_{ϕ} = g - ω^{2} R \cos^{2} ϕ$
As, $ϕ$ increases, $g_{ϕ}$ also increases.
Thus, option (4) is correct but rest are incorrect.

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