A body hanging from a massless spring stretches it by 3 cm on earth's surface. At a place 800 km above the earth's surface, the same body will stretch the spring by (Radius of Earth = 6400 km )

Step-by-step solution

Acceleration due to gravity, g = G M r 2 ∴ g ∝ 1 r 2 When the body is hanged on a spring F = - k x = m g .....(i) Acts on it, where x is extension in spring. Let 800 k m above the Earth's surface, the stretch in the length of spring is x ′ and value of g is g ′ . g = G M R 2 and g ′ = G M R + h 2 So, g ′ = g 1 + h R 2 ....(ii) Where, R = radius of Earth From Equation (i), we get k x = m g ⇒ x ∝ g ......(iii) Therefore, x ′ x = g ′ g From Equations (ii) and (iii), we get x ′ x = g 1 + h R 2 g = g g 1 + 800 × 10 3 64