Question

The acceleration due to gravity at a height $1\text{km}$ above the earth's surface is the same as at a depth $d$ below the surface of earth. Then

• A. $d=\frac{1}{2}\text{km}$
• B. $d=1\text{km}$
• C. $d=\frac{3}{2}\text{km}$
• D. $d=2\text{km}$

Answer 1

The correct option is D $d=2\text{km}$

As we know that above earth surface, the acceleration due to gravity will be

$g^{\prime }=g(1-\frac{2h}{R_e})(\because h<<R)$

$\Rightarrow \Delta g^{\prime }=g\frac{2h}{R_e}........\left(1\right)$

And below earth surface for $d$ depth

$g^{\prime }=g(1-\frac{d}{R_e})$

$\Rightarrow \Delta g^{\prime }=g\frac{d}{R_e}.........\left(2\right)$

From eq. (1) & (2)

$d=2h$

$\Rightarrow d=2\times 1=2\text{km}(\because h=2\text{km})$

Hence, option $\left(d\right)$ is the correct choice.

Why this question ? Tip: The result $g_d=g(1-\frac{d}{R})$ is valid for any value of $d$, small or large.