Section 4: Soil and Water Conservation Engineering
Surveying and Levelling
Subtopic: Types of levelling
Question Statement:
The underside beam of a railway bridge, a permanent Bench Mark with RL 85.168 m, is used for a leveling operation. The Back Sight (staff held inverted against the BM) = 3.645 m. For a Fore Sight of 1.523 m at a construction-site point, find its RL in m (rounded to 2 decimal places).
*(Note: This question was officially CANCELLED / WITHDRAWN by the organizing institute (IIT Delhi) in the official GATE 2020 evaluation, and MARKS TO ALL (MTA) were awarded to all candidates).*
Official Answer Key:
80.00 to 80.00
Step-by-Step Solution & Explanation
[OFFICIAL STATUS NOTE: This question was officially WITHDRAWN / CANCELLED by the organizing institute (IIT Delhi) in the official GATE 2020 evaluation, and MARKS TO ALL (MTA) were awarded to all candidates.]
Technical Solution & Derivation:
• Inverted staff reading: When the leveling staff is held upside-down against an elevated overhead Bench Mark (BM) located above the instrument line of collimation, the Back Sight is entered with a negative sign in leveling reductions.
• Height of Instrument (HI):
$\text{HI} = \text{RL}_{\text{BM}} - \text{BS} = 85.168 - 3.645 = 81.523\text{ m}$
• Reduced Level (RL) of the ground construction point:
$\text{RL}_{\text{point}} = \text{HI} - \text{FS} = 81.523 - 1.523 = 80.000\text{ m}$
• Final calculated value: 80.00 m
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