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A surveyor's 30 m steel tape is correct ...

A surveyor's 30 m steel tape is correct at a temperature of `20^@C`. The distance between two points, as measured by this tape on a day when the temperature is `35^@C`. Is 26m. What is the true distance between the point?
`(a_("steel")=1.2xx10^(-5@)C`)

Text Solution

Verified by Experts

Let temperature rise above the correct temperature rise above the correct temperature by `theta`.
`implies theta=35-20=15^@C`
Using the relation :
Correct length = measured length `(1+alpha theta)implies` true distance between the points
`=26(1+1.2xx10^-5xx15)implies "true distance" =26.00468m`
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