Let ‘gh’ and ‘gd’ be the acceleration due to gravity at height ‘h’ above the earth’s surface and at depth ‘d’ below the earth’s surface respectively. If gh = gd then the relation between ‘h’ and ‘d’ is

Question

Let ‘gh’ and ‘gd’ be the acceleration due to gravity at height ‘h’ above the earth’s surface and at depth ‘d’ below the earth’s surface respectively. If gh = gd then the relation between ‘h’ and ‘d’ is (A) d= h (B) d=(h/2) (C) d=(h/4) (D) d = 2h

Tardigrade Admin · Accepted Answer

Acceleration due to gravity at a height h above the earth’s surface,

g_{h} = g (1 - \frac{2 h}{R})

Acceleration due to gravity at a depth d below the earth’s surface

g_{d} = g (1 - \frac{d}{R})

As

g_{h} = g_{d}

∴ g (1 - \frac{2 h}{R}) = g (1 - \frac{d}{R})

or

1 - \frac{2 h}{R} = 1 - \frac{d}{R} \Rightarrow \frac{2 h}{R} = \frac{d}{R}

\Rightarrow d = 2 h

Q. Let ‘ $g_{h}$ ’ and ‘ $g_{d}$ ’ be the acceleration due to gravity at height ‘ $h$ ’ above the earth’s surface and at depth ‘ $d$ ’ below the earth’s surface respectively. If $g_{h} = g_{d}$ then the relation between ‘ $h$ ’ and ‘ $d$ ’ is

$d = h$

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

$d = \frac{h}{4}$

$d = 2 h$

Q. Let ‘gh​’ and ‘gd​’ be the acceleration due to gravity at height ‘h’ above the earth’s surface and at depth ‘d’ below the earth’s surface respectively. If gh​=gd​ then the relation between ‘h’ and ‘d’ is

d=h

d=2h​

d=4h​

d=2h

Acceleration due to gravity at a height h above the earth’s surface, gh​=g(1−R2h​) Acceleration due to gravity at a depth d below the earth’s surface gd​=g(1−Rd​) As gh​=gd​ ∴g(1−R2h​)=g(1−Rd​) or 1−R2h​=1−Rd​⇒R2h​=Rd​ ⇒d=2h

Q. Let ‘ $g_{h}$ ’ and ‘ $g_{d}$ ’ be the acceleration due to gravity at height ‘ $h$ ’ above the earth’s surface and at depth ‘ $d$ ’ below the earth’s surface respectively. If $g_{h} = g_{d}$ then the relation between ‘ $h$ ’ and ‘ $d$ ’ is

$d = h$

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

$d = \frac{h}{4}$

$d = 2 h$