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A body hanging from a spring stretches i...

A body hanging from a spring stretches it by `2 cm` at the earth's surface. How much will the same body stretch the spring at a place `800 cm` above the earth's surface? Radius of the earth is `6400 km`.

A

0.79 cm

B

1.79 cm

C

0.21 cm

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
(a) As per question, we can write `mg=kx`
`mxx98=kxx1xx10^(2-)`
`implies k=(9.8 m)/(10^(2-))=980 m`
Now, value of g at height 800 km above the earth's surface is g. Hence,
`g'=g(1-(2h)/(R))=9.8(1-(2xx800)/(6400))=9.8(1-(1)/(4))`
`=9.8xx(3)/(4)=(29.4)/(4)`
Again, `m=(29.4)/(4)=kx`
`impliesx=(mxx29.4)/(kxx4)=(mxx29.4)/(4xx980 m)=0.79 cm`
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