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A body hanging from a spring strethces i...

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 1600km above the earth's surface? (Radius of the earth 6400km)

A

1.28 cm

B

0.64 cm

C

3.6 cm

D

0.12 cm

Text Solution

Verified by Experts

The correct Answer is:
B
(b) In equlibrium, weight of the suspended body = stretching force.
`:.` At the earth's surface , `mg=kxx x`
At a height h,mg'`=k xx x'`
`(g')/(g)=(x')/(x)=(R_(e)^(2))/((R_(e)+h)^(2))=((6400)^(2))/((6400+1600)^(2))=((6400)/(8000))^(2)=(16)/(25)`
`x'=(16)/(25)xx x=(16)/(25)xx 1 cm =0.64 cm`
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