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

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

Answer 1

Answer: (A)

$4800 \, km$

Answer 2

$\frac {GM}{R^2}$​[1−$\frac dR$​] = $\frac {4 \times GM}{(4R)^2}$
1−$\frac dR$​ = $\frac 14$
⇒ $\frac dR$​ = $\frac 34$
​⇒ d=$\frac 34$​R
⇒ d= $\frac 34$ x 6400
⇒ d=4800 km

So, the correct option is (A): 4800 km