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A steel tape placed around the earth at ...

A steel tape placed around the earth at the equator when the temperature is `10^(@)C`. What will be the clearance between the tape and the ground (assumed to be uniform) if the temperature of the tape rises to `40^(@)C`? Neglect expansion of the earth. Radius of earth at equator is `6400`km & ` alpha_(steel)= 1.2 xx 10^(-5)K^(-1)`

A

`2.3` m

B

`2.1 ` m

C

`2.3`km

D

`230` m

Text Solution

Verified by Experts

The correct Answer is:
C
Clearance = `R'-R` but `2piR' = 2piR(1+alpha_(s)DeltaT)`
`implies R' - R = R alpha_(s) DeltaT`
=`(6400) (1.2 xx 10^(-5)) (30) = 2.3` km
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