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 the surface of earth. When both 'd' and 'h' are much smaller than the radius of earth, then which one of the following is correct ?

Question

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 the surface of earth. When both 'd' and 'h' are much smaller than the radius of earth, then which one of the following is correct ? (A) d=(h/2) (B) d=(3h/2) (C) d=2 h (D) d=h

Tardigrade Admin · Accepted Answer

gh=g(1-(2 h/R)) ...(i) gd=g(1-(d/R)) ...(ii) From Eqs. (i) and (ii), g(1-(2 h/R))=g(1-(d/R)) ⇒ 2 h=d

Q. 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 the surface of earth. When both ' $d$ ' and ' $h$ ' are much smaller than the radius of earth, then which one of the following is correct ?

$d = \frac{h}{2}$

$d = \frac{3 h}{2}$

$d = 2 h$

$d = h$

$g_{h} = g (1 - \frac{2 h}{R}) ... (i)$
$g_{d} = g (1 - \frac{d}{R}) ... (ii)$
From Eqs. $(i)$ and $(ii)$ ,
$g (1 - \frac{2 h}{R}) = g (1 - \frac{d}{R})$
$\Rightarrow 2 h = d$

Q. 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 the surface of earth. When both 'd' and 'h' are much smaller than the radius of earth, then which one of the following is correct ?

d=2h​

d=23h​

d=2h

d=h