The acceleration due to gravity at a height 1 | vedclass

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(C) The acceleration due to gravity at a height $h$ above the surface of the Earth is given by the formula:$g_h = g \left( 1 - \frac{2h}{R_e} \right)$

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$2$

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(C) The acceleration due to gravity at a height $h$ above the surface of the Earth is given by the formula:$g_h = g \left( 1 - \frac{2h}{R_e} ight)$where $R_e$ is the radius of the Earth.The acceleration due to gravity at a depth $d$ below the surface of the Earth is given by the formula:$g_d = g \left( 1 - \frac{d}{R_e} ight)$According to the problem,the acceleration due to gravity at height $h$ is equal to the acceleration due to gravity at depth $d$:$g_h = g_d$Substituting the formulas:$g \left( 1 - \frac{2h}{R_e} ight) = g \left( 1 - \frac{d}{R_e} ight)$Canceling $g$ from both sides and simplifying:$1 - \frac{2h}{R_e} = 1 - \frac{d}{R_e}$$\frac{2h}{R_e} = \frac{d}{R_e}$$d = 2h$Given that $h = 1\, km$,we find:$d = 2 	imes 1\, km = 2\, km$

The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then $d = $ ......... $km$

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