Question

The value of acceleration due to gravity at a height of $10\,km$ from the surface of earth is $x$. At what depth inside the earth is the value of the acceleration due to gravity has the same value $x$?

• A. 5 km
• B. 20 km
• C. 10 km
• D. 15 km

Answer 1

Answer: (B)

$g_{h}=g\left(1-\frac{2 h}{R}\right)$
$g_{d}=g\left(1-\frac{d}{R}\right) $
$\Rightarrow g_{h}=g_{d}$
$g\left(1-\frac{2 h}{R}\right)=g\left(1-\frac{d}{R}\right) $
$\Rightarrow d=2 h=2 \times 10=20\, km$