Question

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

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

Answer 1

Answer: (A)

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