Question 256: Gravitation

Question

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha \mathrm{h}\left(\mathrm{h}<<\mathrm{R}_{\mathrm{e}}\right)$$ from the earth surface. The value of $$\alpha$$ will be _________.
(use $$\left.\mathrm{R}_{\mathrm{e}}=6400 \mathrm{~km}\right)$$

Accepted Answer

$$g\left( {1 - {{2h} \over R}} \right) = g\left( {1 - {d \over R}} \right)$$
$$ \Rightarrow 2h = d$$
$$ \Rightarrow \alpha  = 2$$

Gravitation

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