1.Q. The distance between the two stations was measured with a 20 m chain and found to be 600 metres. The same was measured with a 30 m chain and found to be 596 metres. If the 20 m chain was 5 cm too short, what was the error in the 30 metre chain? .
Solution:
1. When measured with a 20 m chain
L = 20m . e = 5cm = 0.05 m, too short,
Measurement length ML = 600m
L’ = L – e = 20 – 0.05 = 19.95
True length of the line
TL * (L’)/L * ML = 19.95/20 * 600 = 598.5m
2. When measured with a 30 m chain
L = 30m, ML = 596m, TL = 598.5m
therefore Incorrect length of chain
= L’ ( TL / ML ) x L
= (598.5 / 596 ) x 30
= 30.126 m
Error in 30 m chain,
e = L’ – L
= 30.126 – 30
= 0.126 m, too long.
2Q.A line AB was measured with a chain which is found to be 150 mm too long at the end of measuring a length of 1060 m. What is the true length of the line if the chain used is 20 m at the beginning of the work?
Solution:
Length of chain at the beginning of work, L = 20 m
Error in the length of chain after measuring a distance of =1060m
e = 150mm = 0.15n , too long
therefore Considering mean elongation.
Incorrect length of chain,
L’ = 20 + ((0 + 0.15)/2) = 20.075m
Measured length = ML = 1060m
True length = TL
L/L * ML = (20.075/20 )* 1060 = 1063.975m
True length =_1063.975m