At a certain depth "\(d\)" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3\,R\) above earth surface. Where \(R\) is Radius of earth (Take \(R =6400\,km\) ). The depth \(d\) is equal to \(............\,km\)

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Correct Answer

(D) \(4800\)

Detailed explanation

\(\frac{ GM }{ R ^2}\left[1-\frac{ d }{ R }\right]=\frac{4 \times GM }{(4 R )^2}\)

\(1-\frac{ d }{ R }=\frac{1}{4} \Rightarrow \frac{ d }{ R }=\frac{3}{4} \Rightarrow d \frac{3}{4} R\)

\(d =4800\,km\)

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