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Least Count

Last updated date: 14th Jul 2024
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An Introduction

In the simplest manner, we can define the least count of an instrument as the minimum value that we can measure from it. For example, the smallest distance that we can measure from a meter scale is 1 mm, therefore the least count of the meter scale is 1 mm.

The least count is an indication of the accuracy and precision of the instrument. Lesser is the least count of an instrument higher will be its accuracy.

Least count should not be confused with accuracy, these are two completely different terms. Accuracy is the measure of how close to a certain value an instrument can measure.

Vernier Caliper

Vernier caliper is an instrument introduced by PIERE VERNIER in 1631. It is used for taking a linear measurement with very high accuracy. Vernier Calipers are also used in scientific laboratories due to their high accuracy. 

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Vernier Caliper Comprises of Two Scales

  1. Main Scale- The main scale on the vernier caliper is similar to that on a ruler, graduated in mm and cm on one side; inches on the other is the fixed scale of vernier caliper.

The main scale reading is taken as the first reading on the main scale just before to the left of the zero of the vernier scale.

  1. Vernier Scale- The vernier scale is the movable scale. It moves parallel to the main scale and enables readings to be made even of a fraction of a division on the main scale of the vernier caliper. Vernier scale reading is the mark taken on the vernier scale which exactly coincides with a mark on the main scale

The main scale and vernier scale both contribute to the linear measurement.

According to the previous discussion the main scale reading of the vernier caliper shown in the figure will be = 37 mm

Obtained reading = Main scale reading + Least count * Vernier scale reading 

Uses of A Vernier Calliper

Vernier calipers are used to measure:

  1. The length of a pipe or any object.

  2. The diameter of a spherical ball.

  3. The internal and external diameter of a hollow cylinder can also be measured

Zero Error

When the two jaws are closed if the ‘0’ mark on the main scale and ‘0’ mark on the vernier scale correspond then there is no zero error but otherwise, it is taken into consideration while making linear measurements.

The least count of an instrument having a secondary scale is calculated as follows.

For Vernier Caliper,

  • Smallest reading on the main scale = 1mm

  • Number of divisions on man scale = 10

  • Least count of the main scale = 0.1 mm

  • The secondary scale is the vernier scale. 

  • No. of divisions on the secondary scale = 10

  • Instrument least count = 0.01 mm

FAQs on Least Count

1. What is Vernier Reading?

Vernier reading is the smallest possible measurable distance taken by a Vernier caliper. It is also known as "Resolution". To learn more about the Vernier Caliper and other important topics of the chapter, the student can visit Vedantu’s official website where they’ll find a list of important questions and answers that are highly probable in exams. They can also check out Vedantu’s official Youtube Channel where the student will find video lectures and live Q&A sessions on Vernier Caliper and other topics of all subjects.

2. What is the formula for the Least Count?

Vernier Caliper’s least count is calculated by dividing the smallest reading of the main scale with the total number of divisions on the secondary scale. This was the formula of Least count. To study and score good marks in this topic and other important topics of this chapter, the student should check out the list of important questions prepared by the best teachers at Vedantu. Students can also refer to reference books  RD Sharma and RS Aggarwal for more practice. They can find solutions to Rd Sharma and RS Aggarwal on the Vedantu website.

3. What is a Vernier Caliper?

Vernier caliper is an instrument mainly used for measuring linear dimensions. It is used to measure the diameter of spherical balls of small size. To learn more about Vernier Caliper and other important topics of this chapter, the student can check out the official website of Vedantu. Here, the student can find the list of important questions and answers and also a lot of FREE resources that will help the student to bring good marks. Students can also check out Vedantu’s Youtube Channel where they can attend live sessions with the best teachers of Vedantu and also see previous video lectures. 

4. What are the seven basic units?

The seven basic units of measurement are-

  • Length- A meter is the unit of measurement for length. It is defined as the length of a light's journey during a period of exactly 12997924581299792458 s. It is based on the basic quantity c=299 792 458 m/s, which is the speed of light in a vacuum.

  • Time- The time required by 9 192 631 770 cycles of light oscillations emitted by cesium -133 atoms to transition between two hyper-fine levels of the ground state. High-precision atomic clocks are used to determine this.

  • Mass- A kilogram is a unit of mass. It's the weight of a platinum-iridium cylinder prototype maintained at the International Bureau of Weights and Measures in Paris, France. Many countries have copies of this cylinder, which they use to standardize and compare weights.

  • Electricity- Ampere is a unit of measurement for electric current. The continuous current would create a force of 21072107 Newton per meter of length between two straight parallel conductors of infinite length and insignificant circular cross-section when putting 1 m apart in a vacuum. While it may appear that electric charge should have been used as the basic unit, measuring current is significantly easier, therefore it was selected.

  • Temperature- Kelvin is a unit of temperature (K)Kelvin is the SI unit of temperature. It is 1/273.16 of the thermodynamic temperature of water at its triple point. Water's triple point is a set temperature and pressure at which the solid, liquid, and gaseous phases may coexist.

  • Amount of a substance- The mole is defined as the quantity of stuff that includes the same number of entities as atoms in 0.012 kg of carbon-12. An Avogadro number of entities can be found in a mole. 

  • Luminous Intensity- It is the radiant intensity of a source emitting radiation with a constant frequency of 54010125401012Hz and a radiant intensity of 16831683 Watt per steradian in any direction.

5. What are the different types of errors?

Every measurement has a margin of mistake, which is referred to as an error in the measurement. This error might occur in the processor as a result of an error in the experiment. As a result, no approach can provide 100 percent accurate measurements. The discrepancy between the measured and actual value might be defined as an error. There are three categories of mistakes, each of which is categorized according to the cause of the error-

  • Gross Errors- Goss Errors mostly account for human error and other errors made while reading, recording, and readings. This category of measuring mistakes includes the most prevalent faults, such as human error in measurement. 

  • Random Errors- Random errors are ones that occur seldom and hence are unpredictable. These can occur as a result of random and unpredictable variations in experimental settings

  • Systematic Errors- Systematic errors are again divided into 3 parts-

  • Environmental Errors- Environmental Errors Occur owing to the influence of external factors on the measurement. Temperature, pressure, and humidity are all examples of external conditions, which can also include an external magnetic field.

  • Observational Errors- Observational Errors are mistakes that occur as a result of a person's prejudice, a lack of adequate instrument setup, or silly negligence in handling observations. Wrong readings owing to parallax errors are also included in the measurement errors.

  • Instrumental Errors- Instrumental Errors are caused by defective measurement instrument construction and calibration. These inaccuracies are caused by the equipment's hysteresis or friction. Frequently, the equipment in use is malfunctioning as a result of overuse or neglect, causing the device's reading to shift. A typical sort of mistake is zero error. Devices like vernier calipers and screw gauges are prone to this inaccuracy. It's possible to have a positive or negative zero inaccuracy.