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  4. 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 α h (h ll Re ) from the earth surface. The value of α will be (use Re=6400 km )

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Q. 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 $\alpha h$ (h $\ll R_e$ ) from the earth surface. The value of $\alpha$ will be
(use $R_e=6400 \,km$ )

JEE MainJEE Main 2022Gravitation

Solution:

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