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(B) The gravitational acceleration at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R})$,where $R$ is the radius of the Ea

Vedclass · Accepted Answer

$0.5$

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(B) The gravitational acceleration at a height $h$ above the Earth's surface is given by $g_h = g(1 - \frac{2h}{R})$,where $R$ is the radius of the Earth.The gravitational acceleration at a depth $d$ below the Earth's surface is given by $g_d = g(1 - \frac{d}{R})$.Given that the gravitational accelerations are the same,we equate the two expressions:$g(1 - \frac{2h}{R}) = g(1 - \frac{d}{R})$Canceling $g$ from both sides:$1 - \frac{2h}{R} = 1 - \frac{d}{R}$Subtracting $1$ from both sides:$-\frac{2h}{R} = -\frac{d}{R}$Multiplying by $-R$:$2h = d$Therefore,the ratio of height to depth is:$\frac{h}{d} = \frac{1}{2} = 0.5$

The ratio of the height $h$ above the surface of the Earth to the depth $d$ below the surface of the Earth,for which the gravitational accelerations are the same (assuming small heights),is:

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