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=6400 km). The depth d is equal to

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

5260km

2560 km

4800km

640km

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

We know,

Acceleration due to gravity at a depth d is

$g_{d} = g (1 - \frac{d}{R})$

And acceleration due to gravity at a height h is

$g_{h} = g {(1 + \frac{h}{R})}^{- 2}$

Given in the question

$g_{d} = 4 \times g_{h = 3 R}$

$g [1 - \frac{d}{R}] = 4 g {[1 + \frac{3 R}{R}]}^{- 2}$

$\Rightarrow [1 - \frac{d}{R}] = \frac{1}{4} \Rightarrow d = \frac{3 R}{4}$

d = 4800km

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE