---
title: "Correction per tape length (kg data, 58)"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:tape-base-line-correction-per-tape-58"
source: https://www.bctengineer.com/q/semester_3/surveying_i/tape-base-line-correction-per-tape-58
site: BCT Engineering
---

# Correction per tape length (kg data, 58)

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2058 Chaitra, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/tape-base-line-correction-per-tape-58
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

To lay off a base line, a steel tape 30 m long standardized at 15°C with a pull of 10 kg supported at two ends was used. Find the correction per tape length, if the temperature at the time of measurement was 20°C and pull exerted was 16 kg. Weight of 1 cubic cm of steel is 0.00786 kg. Weight of tape = 0.8 kg, $E = 2.1\times10^{6}$ kg/sq.cm. Coefficient of expansion of the tape per 1°C = $7.1\times10^{-7}$.

## Short answer

Temperature correction = +0.000107 m, pull correction = +0.002526 m, sag correction = -0.003125 m. Total correction per tape length = -0.0005 m (true length 29.9995 m).

## Answer

**Reading.** The tape was standardised with the specified pull (fully supported) and is used supported at the two ends only, so the sag correction applies. Corrections are temperature, pull and sag.

#### Data
- $l = 30$ m; $T_0 = 15^\circ$C, $T = 20^\circ$C; $P_0 = 10$ kg, $P = 16$ kg
- $W = 0.8$ kg; density $= 0.00786$ kg/cm$^3$; $E = 2.1\times 10^{6}$ kg/cm$^2$; $\alpha = 7.1\times 10^{-7}$/$^\circ$C

#### Area of the tape
$$
A = \frac{0.8}{0.00786\times 3000} = 0.03393\ \text{cm}^2,\qquad AE = 0.03393\times 2.1\times 10^{6} = 71{,}247\ \text{kg}
$$

#### 1. Temperature
$$
C_t = 7.1\times 10^{-7}\times 5\times 30 = +0.000107\ \text{m}
$$

#### 2. Pull
$$
C_p = \frac{(16 - 10)\times 30}{71{,}247} = +0.002526\ \text{m}
$$

#### 3. Sag
$$
C_s = -\frac{W^{2}\,l}{24\,P^{2}} = -\frac{0.8^{2}\times 30}{24\times 16^{2}} = -0.003125\ \text{m}
$$

#### 4. Correction per tape length
$$
C = 0.000107 + 0.002526 - 0.003125 = -0.000492\ \text{m}
$$

**Answer: correction per tape length $= -0.0005$ m (about $-0.5$ mm), so the true length of one tape length is 29.9995 m.**

## Check yourself

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

1. Supported at two ends only means
   A. sag correction applies
   B. no sag
   C. no pull
   D. no temp
   Answer: A. Hangs. (Key point: Supports)

2. Sag per tape
   A. +
   B. -W^2 l/(24P^2)
   C. W l
   D. W/P
   Answer: B. Standard. (Key point: Sag formula)

3. Correction is
   A. +
   B. 0
   C. negative, -0.0005 m
   D. +0.0254
   Answer: C. Sag exceeds sum. (Key point: Net)

4. E=2.1e6 kg/cm^2 gives AE
   A. 7124.7
   B. 712,470
   C. 0.03
   D. 71,247 kg
   Answer: D. 0.03393 x 2.1e6. (Key point: E unit)

## Close variants set in other exams

- [Correction per tape length (kgf data, 61)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-base-line-correction-per-tape-61) — Surveying I, chapter 2, asked 2×

## Related in Surveying I

- [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×
- [True length of 780 m line, tape 0.693 kg](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-30m-780m-line) — Surveying I, chapter 2, asked 2×
- [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×
- [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×
- [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×
- [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

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