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?

Similar Questions

In the provided figure of the Earth,the value of acceleration due to gravity is the same at points $A$ and $C$,but it is smaller than its value at point $B$ (surface of the Earth). The value of $OA : AB$ is $x : y$. The value of $x$ is $\ldots \ldots \ldots$

Calculate the difference in the value of $g$ at the equator and at the poles due to the rotation of the Earth.

Give the value of acceleration due to gravity at height $12\, km$ from the surface of earth. (in $, m/s^2$)

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What will be the formula for the mass of the Earth in terms of $g$,$R$,and $G$?

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