Question

The length of a survey line when measured with a chain of \(20\) m nominal length was found to be \(85\) m. If the chain used is \(0.1\) m too long, the correct length of the line is

• A. \(87\) m
• B. \(837.39\) m
• C. \(86\) m
• D. \(839.4\) m

Hint:

If the chain is
• Too long $\rightarrow$ Actual distance is greater than measured distance.
• Too short $\rightarrow$ Actual distance is smaller than measured distance. Use \[ \boxed{ L_c=L_m\left(\frac{l_a}{l_n}\right) } \]

Answer 1

The Correct Option is A

Concept: If the chain is longer than its nominal length, the measured distance is smaller than the actual distance. The correction formula is \[ \boxed{ L_c=L_m\left(\frac{l_a}{l_n}\right) } \] where \[ L_c=\text{Correct length}, \] \[ L_m=\text{Measured length}, \] \[ l_a=\text{Actual chain length}, \] \[ l_n=\text{Nominal chain length}. \]

Step 1: Write the given data. Measured length, \[ L_m=85\text{ m} \] Nominal chain length, \[ l_n=20\text{ m} \] Actual chain length, \[ l_a=20+0.1=20.1\text{ m} \]

Step 2: Calculate the correct length. \[ L_c = 85\left(\frac{20.1}{20}\right) = 85(1.005) = 87075\text{ m} \] Therefore, \[ \boxed{L_c\approx87\text{ m}} \] Hence, the correct option is \[ \boxed{(A)\;87\text{ m}.} \]