A body hanging from a spring stretches it by 1 cm at the earth's surface. How much will the same body stretch the spring at a place 1600 km above the earth's surface? (ans in cm) (Radius of earth = 6400 km )

Step-by-step solution

In equilibrium, weight of the body = stretching force ∴ At the earth's surface, mg ' = k × x ' ⇒ g ' g = x ' x = R e 2 ( R e + h ) 2 = ( 6400 ) 2 ( 6400 + 1600 ) 2 = 16 25 ⇒ x ' = 16 25 × x = 16 25 × 1 cm = 0.64 cm