Question

If value of acceleration due to gravity is ' $g$ ' at a height $50km$ above the surface of earth, then at what depth inside the earth will the acceleration due to gravity be same as ' $g$ '?

• A. $100km$
• B. $50km$
• C. $25km$
• D. $75km$

Answer 1

Answer: (A)

As we know, $g^{\prime }=g\left(1-\frac{2h}{R}\right)=g\left(1-\frac{d}{R}\right)$
$\therefore \frac{2h}{R}=\frac{d}{R}$
$\therefore h=\frac{d}{2}$
or $d=2h$.
$\therefore d=2\times 50=100km$.