---
title: "True length of 780 m line, tape 0.693 kg"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-30m-780m-line"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-30m-780m-line
site: BCT Engineering
---

# True length of 780 m line, tape 0.693 kg

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2073 Shrawan, 8 marks
- Video: [Find the correct length of the line|correction for chain length|length correction](https://www.youtube.com/watch?v=zrthvZDi3VM) — Hamro Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-30m-780m-line
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

A steel tape was exactly 30 m long at 20°C when supported throughout its length under a pull of 10 kg. A line was measured with this tape under a pull of 15 kg and at a mean temperature of 32°C and found to be 780 m long. The cross section area of tape = 0.03 cm² and its total weight = 0.693 kg. $\alpha$ for steel = $11\times10^{-6}$ per °C and $E$ for steel = $2.1\times10^{6}$ kg/cm². Compute the true length of the line if the tape was supported during measurement at every 15 m.

## Short answer

Determine temperature (+0.1030 m), pull (+0.0619 m), and sag corrections for 52 spans of 15 m (-0.0173 m). True length of line is 780.1475 m.

## Answer

**Assumption.** The tape was standardised fully supported ($20^\circ$C, 10 kg), so there is no standard sag to add back.

#### Data
- $L = 780$ m; supports every 15 m, so $780/15 = 52$ spans
- $P_0 = 10$ kg, $P = 15$ kg; $T_0 = 20^\circ$C, $T = 32^\circ$C
- $A = 0.03$ cm$^2$, $E = 2.1\times 10^{6}$ kg/cm$^2$, $\alpha = 11\times 10^{-6}$/$^\circ$C
- $w = 0.693/30 = 0.0231$ kg/m

#### 1. Temperature correction
$$
C_t = 11\times 10^{-6}\times(32 - 20)\times 780 = +0.1030\ \text{m}
$$

#### 2. Pull correction
$$
C_p = \frac{(15 - 10)\times 780}{0.03\times 2.1\times 10^{6}} = +0.0619\ \text{m}
$$

#### 3. Sag correction
Per span: $\dfrac{0.0231^{2}\times 15^{3}}{24\times 15^{2}} = 0.000334$ m.

$$
C_s = -52\times 0.000334 = -0.0173\ \text{m}
$$

#### 4. True length
$$
L_{true} = 780 + 0.1030 + 0.0619 - 0.0173 = 780.1475\ \text{m}
$$

**Answer: true length of the line $= 780.1475$ m.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is w obtained?
   A. Total weight 0.693 kg divided by 30 m = 0.0231 kg/m
   B. 0.693 x 30
   C. 0.693/780
   D. 0.693 x 0.03
   Answer: A. Weight of tape divided by its length. (Key point: Weight per metre)

2. The temperature correction is
   A. Negative since pull is larger
   B. + alpha (T - T0) L, positive since 32 > 20
   C. Zero
   D. - alpha (T - T0) L
   Answer: B. Hotter tape is longer, so the reading is too small and is increased. (Key point: Temperature correction)

3. With supports every 15 m, the number of spans is
   A. 26
   B. 78
   C. 52
   D. 780
   Answer: C. 780/15 = 52. (Key point: Spans)

4. Which correction is negative?
   A. Pull
   B. Temperature
   C. Both pull and temperature
   D. Sag
   Answer: D. Only sag is subtracted; temperature and pull are positive here. (Key point: Net effect)

## Close variants set in other exams

- [True length of 680 m line, 20 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-680m-line) — Surveying I, chapter 2, asked 3×

## Related in Surveying I

- [True length: tape found 2.5 cm too long](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-825-plus-750-m) — Surveying I, chapter 2
- [True length of 1020 m line, 20 m tape](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-1020m-line) — Surveying I, chapter 2, asked 2×
- [Tape corrections for 86 m, 15 kg pull](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-86m-supports-10m-15kg) — Surveying I, chapter 2, asked 3×
- [Tape corrections for 86 m, 10 kg pull](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-20m-86m-pull-10kg) — Surveying I, chapter 2, asked 3×
- [Correction per tape length (kg data, 58)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-base-line-correction-per-tape-58) — Surveying I, chapter 2, asked 2×
- [True length of 358.650 m line](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-358-650-m-line) — Surveying I, chapter 2