Question

An iron rod of length 100 m at 10°C is usedto measure a distance of 2 km on a day when the temperature is 40°C. Calculate the error in measuring the distance.
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Answer 1

assuming α be the thermal expansion coefficient.

so at 40°C the length of rod will be.

100 *α *(40-10) = 3000α

to measure 2Km we need to move 100m rod 20 times

so final measurement will be 3000 α * 20 = 60000α

divide it by 1000 to convert it to meters = 60α

original length 2Km

measured length = 60α

change = 60α - 2

error in calculation = (60α - 2)/2

the answer totally depend upon alpha.

Answer 2

The error in measurement is 0.68m

Given :

Length of iron rod = 100m

Temperature =10°C

Distance = 2km

Temperature = 40°C

To find :

the error in measuring the distance

Solution :

We know that when an object is heated or cooled, its length changes by an amount dl which is proportional to the original length Lo and the change in temperature Δt.

This can be expressed as

$dl = Lo \: \alpha (tf - ti)......(i)$

where α is coefficient of linear expansion, ti initial temperature and tf .

Taking α for for iron rod as 1.13×10^−5 K^-1 change in length of rod is

dl = 100 x 1.13 x 10^-5(40-10)

dl = 0.0339m

Distance measured = 2000m

Error in measurement =( 2000/(100+0.0339) ) x 0.0339

= 0.68m

Hence, the error in measurement is 0.68 m

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