# Levelling and Contouring

 Question 1
Trigonometric levelling was carried out from two stations $P$ and $Q$ to find the reduced level (R.L.) of the top of hillock, as shown in the table. The distance between stations $P$ and $Q$ is $55 \mathrm{~m}$. Assume stations $P$ and $Q$, and the hillock are in the same vertical plane. The R. L. of the top of the hillock (in$\mathrm{m}$ ) is _____ (round off to three decimal places)
$\begin{array}{|l|l|l|l|} \hline Station &\begin{array}{c}\text{Vertical} \\ \text{angle of} \\ \text {the top of} \\ \text{hillock }\end{array} &\begin{array}{c}\text {Staff} \\ \text{reading} \\ \text {on} \\ \text{benchmark}\end{array} &\begin{array}{c}\text {R.L. of} \\ \text {benchmark}\end{array} \\ \hline P &18^{\circ} 45^{\prime} &2.340 \mathrm{~m} &100.000 \mathrm{~m} \\ \hline Q &12^{\circ} 45^{\prime} &1.660 \mathrm{~m}& \\ \hline \end{array}$
 A 124.365 B 137.682 C 253.142 D 254.325
GATE CE 2023 SET-1   Geomatics Engineering
Question 1 Explanation:

While taking reading from $P$,
RL of hillock $=H I_P+x \tan 18^{\circ} 45^{\prime}$
$=100+2.34+x \tan 18^{\circ} 45^{\prime}$

While taking reading from $Q$.
$\mathrm{RL}$ of hillock $=\mathrm{HI}_Q+(\mathrm{x}+55) \tan 12^{\circ} 45^{\prime}$
$=100+1.66+(x +55)\tan 12^{\circ} 45^{\prime}$
Equating both,
$100+2.34+x \tan 18^{\circ} 45^{\prime}=100+1.66+(x +55)\tan 12^{\circ} 45^{\prime}$
$2.34+0.339 x=1.66+12.445+0.226 x$
$\therefore x=104.115$

$\quad \therefore \quad$ RL of hillock
$=100+2.34+104.115 \tan 18^{\circ} 45^{\prime}$
$=137.682$
 Question 2
Which of the following is NOT a correct statement?
 A The first reading from a level station is a 'Fore Sight' B Basic principle of surveying is to work from whole to parts C Contours of different elevations may intersect each other in case of an overhanging cliff D Planimeter is used for measuring 'area'
GATE CE 2021 SET-1   Geometics Engineering
Question 2 Explanation:
First reading from level station is called BS.

 Question 3
A level instrument at a height of 1.320 m has been placed at a station having a Reduced Level (RL) of 112.565 m. The instrument reads -2.835 m on a levelling staff held at the bottom of a bridge deck. The RL (in m) of the bottom of the bridge deck is
 A 116.72 B 116.08 C 114.08 D 111.05
GATE CE 2018 SET-2   Geomatics Engineering
Question 3 Explanation:

\begin{aligned} &\text { RL of bottom of bridge deck }\\ &=112.565+1.320+(2.835)\\ &=116.720 \mathrm{m} \end{aligned}
 Question 4
The vertical angles subtended by the top of a tower T at two instrument stations set up at P and Q, are shown in the figure. The two stations are in line with the tower and spaced at a distance of 60m. Readings taken from these two stations on a leveling staff placed at the benchmark (BM = 450.000 m) are also shown in the figure. The reduced level of the top of the tower T (expressed in m) is _____ .
 A 450.25 B 474.35 C 24.35 D 476.91
GATE CE 2016 SET-1   Geomatics Engineering
Question 4 Explanation:

\begin{aligned} \ln \Delta B E T \\ \tan 16.5^{\circ}&=\frac{x}{y}\\ \Rightarrow \quad y&=3.3759 x &\ldots(i)\\ In \triangle A O T \\ \tan 10.5&=\frac{x+2}{60+y}&\ldots(ii) \end{aligned}
Put value of y in eq. (ii)
\begin{aligned} 0.1853&=\frac{x+2}{60+3.3759 x} \\ 11.1203+&0.6255 x=x+2 \\ x=& 24.3588 \mathrm{m} \end{aligned}
So, the reduced level of tower
\begin{aligned} T&=450.000+2.555+24.358\\ &=476.911 \mathrm{m} \end{aligned}
 Question 5
The staff reading taken on a workshop floor using a level is 0.645 m. The inverted staff reading taken to the bottom of a beam is 2.960 m. The reduced level of the floor is 40.500 m. The reduced level (expressed in m) of the bottom of the beam is
 A 44.105 B 43.46 C 42.815 D 41.145
GATE CE 2016 SET-1   Geomatics Engineering
Question 5 Explanation:
Height of instrument, HI
A.L. of floor + stall reading from floor
$\begin{array}{l} =40.500+0.645 \\ =41.145 \mathrm{m} \end{array}$
R.L. of bottom of beam =H / 4 inverted staff reading taken from bottom of beam
$\begin{array}{l} =41.145+2.800 \\ =44.105 \mathrm{m} \end{array}$

There are 5 questions to complete.

### 5 thoughts on “Levelling and Contouring”

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