1 \(d=R\left(\dfrac{n}{n-1}\right)\)
2 \(d=R\left(\dfrac{n-1}{2 n}\right)\)
3 \(d=R\left(\dfrac{n-1}{n}\right)\)
4 \(d=R^{2}\left(\dfrac{n-1}{n}\right)\)
Explanation:
Acceleration due to gravity at depth \(d\) is given as
\({g^\prime } = g\left( {1 - \frac{d}{R}} \right){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,\,\,\,\,\,\,\,(1)\)
Given, \(g^{\prime}=\dfrac{g}{n}\)
Substituting the value of ' \(g\) ' in eq.(1), we get
\(\begin{aligned}& \dfrac{g}{n}=g\left(1-\dfrac{d}{R}\right) \\& \Rightarrow \dfrac{1}{n}=1-\dfrac{d}{R}\end{aligned}\)
\(\Rightarrow d=R\left(\dfrac{n-1}{n}\right)\)