The change in the value of g at a height h ab | vedclass

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(D) The variation of acceleration due to gravity $g$ with altitude $h$ (where $h \ll R$) is given by: $g_h = g(1 - \frac{2h}{R})$.The variation of acc

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$d = 2h$

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(D) The variation of acceleration due to gravity $g$ with altitude $h$ (where $h \ll R$) is given by: $g_h = g(1 - \frac{2h}{R})$.The variation of acceleration due to gravity $g$ with depth $d$ (where $d \ll R$) is given by: $g_d = g(1 - \frac{d}{R})$.According to the problem,the change in the value of $g$ at height $h$ is the same as the change at depth $d$. This implies that the values of $g$ at these points are equal,so $g_h = g_d$.Equating the two expressions: $g(1 - \frac{2h}{R}) = g(1 - \frac{d}{R})$.Simplifying the equation: $1 - \frac{2h}{R} = 1 - \frac{d}{R}$.Subtracting $1$ from both sides: $-\frac{2h}{R} = -\frac{d}{R}$.Multiplying by $-R$: $d = 2h$.

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of the earth. When both $d$ and $h$ are much smaller than the radius of the earth,then which one of the following is correct?

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