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Question

In levelling between two points P and Q on opposite banks of a river, the level was set up near P, and the staff reading on P and Q were 2.165 m and 3.810 m, respectively. The level was then moved and set up near Q and the respective staff readings on P and Q were 0.910 m and 2.355 m. The true difference of level between P and Q is __________ m (rounded off to 3 decimal places).

The problem involves determining the true difference in level between two points, P and Q, across a river using a technique called reciprocal leveling. We have two sets of staff readings from different positions of the level instrument. To find the true difference in level, we need to calculate the average of the differences observed from each position.
Step 1: Calculate the initial difference from P

When the level is near P, the reading on P is 2.165 m and on Q is 3.810 m. The difference in this setup is:

Difference 1 = 3.810 m - 2.165 m = 1.645 m

Step 2: Calculate the reverse difference from Q

When the level is moved near Q, the reading on P is 0.910 m and on Q is 2.355 m. The difference in this setup is:

Difference 2 = 2.355 m - 0.910 m = 1.445 m

Step 3: Compute the true difference in level

The average of the two differences gives the true difference in level between P and Q:

True Difference = (1.645 m + 1.445 m) / 2 = 1.545 m

Step 4: Validate the result

The computed true difference in level is 1.545 m. This value must fall within the given range of 1.54 to 1.55 m, which it does:

1.540 ≤ 1.545 ≤ 1.550

Therefore, the true difference in level between P and Q is 1.545 m, confirmed to be within the specified range.
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Important Questions from Levelling Methods

  1. Which one of the following is the purpose of taking a backsight observation in levelling?
  2. The observations of a reciprocal levelling operation carried out from two stations A and B are given in table. It is known that the instrument has collimation error. The correct staff reading over station B when the instrument is set very near to station A is ________ m (Rounded off to three decimal places).

    Assume all other errors are negligible.

    Staff readings at station
    Instrument set very near to stationA (m)B (m)
    A1.2752.005
    B1.0401.660
  3. A level with the height of the instrument being 2.550 m has been placed at a station having a Reduced Level (RL) of 130.565 m. The instrument reads 3.665 m on a levelling staff held inverted at the bottom of a bridge deck. The RL of the bottom of the bridge deck is __________ m (rounded off to 3 decimal places).
  4. Change Point (CP) in levelling refers to a location where
  5. At a fixed instrument location in levelling, if the backsight reading at a point P is more than the foresight reading at a point Q, then
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