Physics · Units And Measurements · NEET
Both meanings are correct and connected. The least count is the smallest value you can read on the instrument, and it is also the smallest error the instrument can have in a single reading. Example: a normal metre scale has a least count of 1 mm, so you can read down to 1 mm, and your smallest possible uncertainty in one reading is about 1 mm. For NEET, remember: least count = smallest measurable value = limit of precision.
The general rule is: Least Count = value of one main scale division / number of divisions on the moving (finer) scale. For a vernier caliper: Least Count = 1 MSD − 1 VSD, which equals (value of 1 MSD) / (number of vernier divisions). For a screw gauge: Least Count = Pitch / number of divisions on the circular scale, where Pitch = distance the screw moves in one full rotation. Always convert to the same unit before dividing.
A smaller least count means the instrument can detect smaller changes in length. A metre scale (least count 1 mm) cannot tell the difference between 2.34 cm and 2.35 cm, but a screw gauge (least count 0.01 mm) can. So a smaller least count gives you more decimal places and less uncertainty. This is why NEET numericals use vernier callipers and screw gauges for tiny objects like wires and balls.
Pitch is only for a screw gauge. Pitch is the distance the screw moves forward in ONE complete rotation of the circular scale. Least count is smaller than pitch: Least Count = Pitch / number of circular scale divisions. Example: Pitch = 0.5 mm and 50 circular divisions gives Least Count = 0.5/50 = 0.01 mm. So pitch is the big step per full turn, least count is the tiny step per one division.
An ordinary metre scale (ruler) has millimetre marks, so its least count is 1 mm = 0.1 cm = 0.001 m. This is why you cannot measure the diameter of a thin wire with a metre scale; its least count is too large. For finer measurements NEET expects vernier callipers (least count around 0.01 cm) or a screw gauge (least count around 0.001 cm).
No. Zero error and least count are separate things. Least count depends only on the instrument's scale divisions; it never changes for a given instrument. Zero error is a fixed shift you add or subtract from your reading. In a PYQ you first find the least count from the scale, then apply the zero-error correction to the final reading. They are calculated at two different steps.
The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with (n−1) divisions of the main scale. The least count of the vernier calliper is:
In a vernier callipers, (N+1) divisions of the vernier scale coincide with N divisions of the main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:
In a vernier calliper, 20 VSD coincide with 16 MSD (each division of length 1 mm). The least count of the vernier calliper is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Least count is the smallest value a measuring instrument can measure, equal to one smallest division on its scale.
A common vernier caliper has a least count of 0.1 mm = 0.01 cm, found from Least Count = 1 MSD − 1 VSD. It varies with the instrument's design.
A typical screw gauge has a least count of 0.01 mm = 0.001 cm, found from Least Count = Pitch / number of circular scale divisions, for example 0.5 mm / 50 = 0.01 mm.
A smaller least count means higher precision and a smaller measurement error. So a screw gauge (0.01 mm) is more precise than a vernier caliper (0.1 mm), which is more precise than a metre scale (1 mm).
Only for a simple ruler. For a vernier or screw gauge, the least count is much smaller than one main division because the finer scale splits that division into many parts.
NEET Units and Measurements almost every year gives a vernier or screw gauge problem where you must first find the least count before reading the value, so the formula is high-yield.
