Question

A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m. The corrected horizontal length (in m) of the line PQ will be:

• A. 342.52
• B. 349.30
• C. 356.20
• D. 350.70

Hint:

When correcting measurements on slopes, use Pythagoras' theorem to find the horizontal distance and correct for tape length when necessary.

Answer 1

The Correct Option is A

Given the measured length between stations P and Q as 350 m, we need to find the corrected horizontal length. We are given: - The slope of 1 in 5, meaning for every 5 m of horizontal distance, the vertical drop is 1 m. - The tape is short by 0.1 m for every 50 m. Step 1: Calculate the vertical distance due to slope. The slope is 1 in 5, so the vertical drop is: \[ \text{Vertical distance} = \frac{1}{5} \times 350 = 70 \, \text{m}. \] Step 2: Correct for the length of the tape. The tape is short by 0.1 m for every 50 m. Since the measured length is 350 m, the correction for the tape length is: \[ \text{Tape correction} = \frac{350}{50} \times 0.1 = 0.7 \, \text{m}. \] So, the corrected length is: \[ \text{Corrected length} = 350 + 0.7 = 350.7 \, \text{m}. \] Step 3: Calculate the corrected horizontal length. Using Pythagoras' theorem, the horizontal length \( L_{\text{horizontal}} \) is given by: \[ L_{\text{horizontal}} = \sqrt{350.7^2 - 70^2} \approx 342.52 \, \text{m}. \] Thus, the corrected horizontal length of the line PQ is approximately 342.52 m. Final Answer: (A) 342.52