A body hanging from a spring strethces it by 1cm at the earth's surface. How much will the same body stretch the spring at a place 16400km above the earth's surface? (Radius of the earth 6400km)

Options

A. `1.28m`
B. `0.64m`
C. `3.6m`
D. `0.12m`

Answer

B

Explanation

In equilibrium, weight of the suspended body = stretching force.
At the earth's surface, `mg=kxxx`
At a height `h, mg'=kxx x'`
`(g')/g=(x')/x=(R_(e)^(2))/((R_(e)+h)^(2))=((6400)^(2))/((6400+1600)^(2))`
`=(6400/8000)^(2)=16/25`
`x'=16/25xx x=16/25xx1 cm=0.64 cm`