Question

If the change in the value of '$g$' at a height $h$ above the surface of the earth is the same as at a depth $d$ below it. When both $d$ and $h$ are much smaller than the radius of earth, then

• A. $d=h$
• B. $d=2h$
• C. $d=h/2$
• D. $d=h$${}^2$

Answer 1

Answer: (B)

$d=2h$

the value of 'g' at a height $h$ above the surface of the earth, $g_h=g(1-\frac{2h}{R})$
the value of 'g' at a depth d, $g_d=g(1-\frac{d}{R})$
But, $g_h=g_d$
$\therefore$ $1-\frac{2h}{R}=1-\frac{d}{R}$
or, $d=2h$