Question

At what depth below the surface of the earth will acceleration due to gravity g be half its value 1600 km above the surface of the earth?

विकल्प

• 4.35 × 10⁶ m

• 3.19 × 10⁶ m

• 1.59 × 10⁶ m

• 4.35 × 10⁵ m

Answer 1

4.35 × 10⁶ m

Explanation:

Radius of earth, R = 6400 km

∴ h = `R/4`

Gravitational acceleration at a height h,

g_h = `g(R/(R + h))^2 = g(R/(R + R/4))^2 = 16/25` g

At depth 'd,' the value of gravity's acceleration

g_d = `1/2` g_h   ......(Given)

∴ g_d = `1/2(16/25)g` 

∴ `g(1 - d/R) = 1/2(16/25)g`

∴ `1 - 16/50 = d/R`

∴ d = `(34 xx 6400 xx 10^3)/50`

∴ d = 4.35 × 10⁶ m