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Error and Uncertainty

A 30 m chain ...

Question

A 30 m chain used to measure the length of a line was tested before the line was measured and found to be 29.95 m long. The line was measured and length was recorded as 590.48 m. The chain was tested again and found to be 30.08 m long. Find the true length of the line(in m)
590.78

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Solution

The correct option is A 590.78
The length of the chain would have changed gradually during measurement and hence the average length of the chain must be used to find the true length.

The average length of the chain

$(\frac{29.95 + 30.08}{2}) = 30.015 m$

$T r u e l e n g t h = M e a s u r e d l e n g t h \times \frac{A c t u a l l e n g t h}{D e s i g n a t e d l e n g t h}$

$= 590.48 \times \frac{30.015}{30} = 590.78 m$

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