Theodolite MCQ with answer and solution

Concept

Least count is the smallest angle that can be read directly on the instrument. Theodolites read angles in degrees, minutes and seconds, and precise or modern theodolites read to about 1 second.

Formula

Least count = value of one main scale division / number of vernier divisions

Step-by-step solution

1. A theodolite measures angles, so its least count is in angle units (degree, minute, second). 2. 'Hour' and 'millisecond' are time units, so C and D are out. 3. A common vernier theodolite: main scale division = 20' and 60 vernier divisions, so LC = 20'/60 = 20 seconds. 4. Micrometer and digital theodolites read to 1 second. 5. Among the options, the angle reading of a theodolite is taken to seconds, so the best answer is 1 second (B).

Explanation

Least count is the smallest angle a theodolite can read. An ordinary vernier transit theodolite reads 20 seconds, and precise or electronic theodolites read 1 second. So among the given options, 1 second is the best choice.

Why the other options are wrong

A: 1 minute is too coarse for most theodolites (usual vernier LC is 20 seconds). C: hour is a time unit, not an angle reading of a theodolite. D: millisecond is a time unit and is not used for angle reading.

Shortcut

Vernier theodolite LC = 20 seconds. Micrometer or digital theodolite = 1 second.

Common mistake

Mixing up the theodolite least count with the compass least count (prismatic compass = 30 minutes, surveyor's compass = 15 minutes).