A spring is stretched by 2 cm by an object attached to It near the surface of earth. How much extension of the same spring take place by the same object when taken to a point 3,200 km above the surface of earth (Radius of earth = 6,400 km)

Options

A. 0.5 cm
B. 0.4 cm
C. 0.9 cm
D. 0.9 cm

Answer

C

Explanation

On the surface of earth, `mg = k (2 cm)`
At a height of 3, 200 km above earth.s surface `mg. = k (y)`
As `g = (GM)/(R^(2))`
`g. = (GM)/((R+h)^(2))`
`(g.)/(g) = (k y)/(k (2)) = (R^(2))/((R+h)^(2))`
`y = (2 cm)((R )/((R+h)))^(2)`
`= 2cm ((6,400 km)/(6,400 km + 3,200 km))^(2)`
`= 2((6,400)/(9,600))^(2) = 0.9 cm`