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7.Gravitation
medium
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 $............\,km$
A
$5260$
B
$640$
C
$2560$
D
$4800$
(JEE MAIN-2023)
Solution
$\frac{ GM }{ R ^2}\left[1-\frac{ d }{ R }\right]=\frac{4 \times GM }{(4 R )^2}$
$1-\frac{ d }{ R }=\frac{1}{4} \Rightarrow \frac{ d }{ R }=\frac{3}{4} \Rightarrow d \frac{3}{4} R$
$d =4800\,km$
Standard 11
Physics
