The value of acceleration due to gravity at a height of 10 km from the surface of earth is x. At what depth inside the earth is the value of the acceleration due to gravity has the same value x?

Question

The value of acceleration due to gravity at a height of 10 km from the surface of earth is x. At what depth inside the earth is the value of the acceleration due to gravity has the same value x? (A) 5 km (B) 20 km (C) 10 km (D) 15 km

Tardigrade Admin · Accepted Answer

gh=g(1-(2 h/R)) gd=g(1-(d/R)) ⇒ gh=gd g(1-(2 h/R))=g(1-(d/R)) ⇒ d=2 h=2 × 10=20 km

Q. The value of acceleration due to gravity at a height of $10 km$ from the surface of earth is $x$ . At what depth inside the earth is the value of the acceleration due to gravity has the same value $x$ ?

5 km

20 km

10 km

15 km

$g_{h} = g (1 - \frac{2 h}{R})$
$g_{d} = g (1 - \frac{d}{R})$
$\Rightarrow g_{h} = g_{d}$
$g (1 - \frac{2 h}{R}) = g (1 - \frac{d}{R})$
$\Rightarrow d = 2 h = 2 \times 10 = 20 km$

Q. The value of acceleration due to gravity at a height of 10km from the surface of earth is x. At what depth inside the earth is the value of the acceleration due to gravity has the same value x?