Q. At what height from the ground will the value of $'g'$ be the same as that in $10\ km$ deep mine below the surface of earth
A) $20\ km$
B) $10\ km$
C) $15\ km$
D) $5\ km$
Explanation
(d) $g^{'}\left( 1 - \frac{d}{R} \right) = g^{'}\left( 1 - \frac{2h}{R} \right)$
d = depth of mine
h = height from surface
$\therefore g^{'}\left( 1 - \frac{d}{R} \right) = g^{'}\left( 1 - \frac{2h}{R} \right)$
$\Rightarrow d = 2h$
$\Rightarrow 10 = 2h$
$\Rightarrow h = 5km$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.