The depth at which acceleration due to gravit | vedclass

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(D) The gravitational acceleration at a depth $d$ below the Earth's surface is given by the formula: $g_d = g \left(1 - \frac{d}{R}\right)$.Given that

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$\frac{R(2n-1)}{2n}$

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(D) The gravitational acceleration at a depth $d$ below the Earth's surface is given by the formula: $g_d = g \left(1 - \frac{d}{R}\right)$.Given that the acceleration due to gravity at depth $d$ is $g_d = \frac{g}{2n}$.Substituting this into the formula:$\frac{g}{2n} = g \left(1 - \frac{d}{R}\right)$.Dividing both sides by $g$:$\frac{1}{2n} = 1 - \frac{d}{R}$.Rearranging the terms to solve for $d$:$\frac{d}{R} = 1 - \frac{1}{2n}$.$\frac{d}{R} = \frac{2n - 1}{2n}$.Therefore,$d = R \left(\frac{2n - 1}{2n}\right)$.

The depth at which acceleration due to gravity becomes $\frac{g}{2n}$ is ($R=$ radius of earth,$g=$ acceleration due to gravity on earth's surface,$n$ is an integer).

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