Question

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 $3R$ above earth surface. Where $R$ is Radius of earth (Take $R=6400km$ ). The depth $d$ is equal to

• A. $4800km$
• B. $640km$
• C. $2560km$
• D. $5260km$

Answer 1

Answer: (A)

$\frac{GM}{R^2}\left[1-\frac{d}{R}\right]=\frac{4\times GM}{(4R{)}^2}$
$1-\frac{d}{R}=\frac{1}{4}\Rightarrow \frac{d}{R}=\frac{3}{4}\Rightarrow d\frac{3}{4}R$
$d=4800km$