Examoogle
ExamsTest SeriesCBATRank CheckPrevious Year PapersPassBook StoreMy BooksAI Tutor
ЁЯЫТ0
рдЕA
Examoogle

India's most trusted platform for competitive exam PDF books. Expert-authored, watermark-protected, instant access.

Exams & Practice
All Exams & SyllabusMock Test SeriesPrevious Year PapersPractice Questions (MCQs)Recruitment Notifications
Quick Links
Examoogle AI TutorExam NewsBook StoreMy BooksLogin / Sign Up
Support
About UsRefund PolicyPrivacy PolicyTerms of UseContact Us
┬й 2026 Examoogle. India's #1 competitive exam AI tutor.
ЁЯФТ SSL SecuredЁЯУ▒ UPI AcceptedЁЯз╛ GST Invoice
Examoogle

Join 60,000+ competitive exam aspirants

or with email
By continuing, you agree to ourTerms of Service&Privacy Policy
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Back to Practice Questions
CivilAdvanced Survey
PrevNext

Calculate the value of K and C, if the measurements are taken between two points of 50m and 130m distance apart and the stadia readings will be 0.024m, 0.824m respectively.

A

100, 0

B
  1. 47.6 100, 47.6
C

47.6, 100

D

0, 100

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilAdvanced Survey
Option B
  1. 47.6

100, 47.6

Quick Summary:

In tacheometric surveying, the horizontal distance DDD between the instrument station and the staff station is given by the distance equation D=Ks+CD = Ks + CD=Ks+C, where KKK is the multiplying constant (f/if/if/i) and CCC is the additive constant (f+df + df+d). Using the two given conditions with staff intercept sss and distance DDD, simultaneous equations are solved to determine K=100K = 100K=100 and C=47.6┬аmC = 47.6\text{ m}C=47.6┬аm.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

In tacheometric surveying, the horizontal distance DDD between the instrument station and the staff station is given by the distance equation D=Ks+CD = Ks + CD=Ks+C, where KKK is the multiplying constant (f/if/if/i) and CCC is the additive constant (f+df + df+d). Using the two given conditions with staff intercept sss and distance DDD, simultaneous equations are solved to determine K=100K = 100K=100 and C=47.6┬аmC = 47.6\text{ m}C=47.6┬аm.

ЁЯФв Key Formulas

D=Ks+CD = Ks + CD=Ks+C тАФ General tacheometric distance equation

K=fiK = \frac{f}{i}K=ifтАЛ тАФ Multiplying constant

C=f+dC = f + dC=f+d тАФ Additive constant

K=D2тИТD1s2тИТs1K = \frac{D_2 - D_1}{s_2 - s_1}K=s2тАЛтИТs1тАЛD2тАЛтИТD1тАЛтАЛ тАФ Formula to derive KKK from two observation points

тЪЩя╕П Working Principle

Tacheometry relies on the principle of isosceles triangles, where the ratio of the distance from the vertex to the base and the length of the base remains constant. The stadia hair readings give the staff intercept sss, which when multiplied by the multiplying constant KKK and added to the additive constant CCC yields the horizontal distance DDD.

ЁЯУМ Key Points
  • тЦ╕

    The multiplying constant KKK is typically equal to 100100100 in an ideal tacheometer equipped with an anallactic lens.

  • тЦ╕

    The additive constant CCC varies according to telescope design, but reduces to 000 when an anallactic lens is fitted.

  • тЦ╕

    Subtracting equation (i) from equation (ii) yields 130тИТ50=K(0.824тИТ0.024)тЗТ80=K(0.800)тЗТK=100130 - 50 = K(0.824 - 0.024) \Rightarrow 80 = K(0.800) \Rightarrow K = 100130тИТ50=K(0.824тИТ0.024)тЗТ80=K(0.800)тЗТK=100.

  • тЦ╕

    Substituting K=100K = 100K=100 into equation (i): 50=100(0.024)+CтЗТ50=2.4+CтЗТC=47.6┬аm50 = 100(0.024) + C \Rightarrow 50 = 2.4 + C \Rightarrow C = 47.6\text{ m}50=100(0.024)+CтЗТ50=2.4+CтЗТC=47.6┬аm.

тЬЕ Advantages
  • тЦ╕

    Allows direct determination of horizontal distance without using physical measuring tapes.

  • тЦ╕

    Particularly suitable for steep, rough, or inaccessible terrains.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Accuracy depends strongly on precise staff intercept measurements.

  • тЦ╕

    Observational errors in staff reading lead directly to distance inaccuracies.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Contour mapping and topographic surveying.

  • тЦ╕

    Preliminary route location surveys for roads, railways, and canals.

ЁЯУД Additional Information
  • тЦ╕

    Option A (100, 0) represents an anallactic telescope where the additive constant C=0C = 0C=0.

  • тЦ╕

    Option C (47.6, 100) reverses the values of KKK and CCC, which is incorrect.

  • тЦ╕

    Option D (0, 100) is invalid as KKK cannot be zero for meaningful distance measurement.

ЁЯУК Diagram / Illustration
Tacheometric Distance Formula CardHorizontal Distance Equation: D = K ├Ч s + CK = Multiplying Constant (f/i) | C = Additive Constant (f + d) | s =Staff InterceptCase 1: DтВБ = 50 m, sтВБ = 0.024 m50 = K(0.024) + C тФАтФА (i)Case 2: DтВВ = 130 m, sтВВ = 0.824 m130 = K(0.824) + C тФАтФА (ii)
тЬЕ

B is correct тАФ Solving 50=0.024K+C50 = 0.024K + C50=0.024K+C and 130=0.824K+C130 = 0.824K + C130=0.824K+C simultaneously yields K=100K = 100K=100 and C=47.6┬аmC = 47.6\text{ m}C=47.6┬аm.

Core Concepts Used
Click any tag to open in AI Tutor
Tacheometric Surveying Multiplying and Additive Constants Stadia Hair Method
ЁЯТб EXAM TIP

Remember that if an anallactic lens is provided in the tacheometer telescope, K=100K = 100K=100 and C=0C = 0C=0 directly, eliminating the additive term.

Related Questions

CivilAdvanced Survey
From a station, we measured as many objects as possible within the sight, that method called to__.
CivilAdvanced Survey
In which are not scale factor in total station ?
CivilAdvanced Survey
How many counts are scale factors in total station ?
CivilAdvanced Survey
Which of the following fundamental parameter for total station?
CivilAdvanced Survey
Which type of method has used in conventional surveying for recording data ?

Discussion (0)

Loading discussion...
PrevNext