1.7.2 Vernier Caliper

In physics and engineering, we often need to measure lengths smaller than 1 mm, such as the thickness of a wire or the diameter of a small ball. A standard metre rule cannot measure such small values accurately. For this purpose, a more precise instrument called the vernier caliper is used.

Definition

A vernier caliper is a measuring device used to measure a fraction of the smallest division on a main scale by sliding another scale over it. It can be used to measure the thickness, diameter, or width of an object, as well as the internal and external diameter of a hollow cylinder.

Main Idea

The main idea is precision through a secondary scale. While a metre rule is limited to measuring to the nearest millimetre (1 mm), a vernier caliper uses a clever sliding scale (the vernier scale) to measure a fraction of a millimetre. This allows for much more precise measurements, typically down to 0.1 mm or even smaller. The instrument is designed to provide accurate measurements of small dimensions that are critical in science and engineering.

Core Concept

• Main Scale: A fixed scale with markings, usually of 1 mm each. It has a fixed jaw on its left end.
• Vernier Scale: A sliding scale that moves over the main scale. It has markings that are a fraction of the size of the markings on the main scale.

Least Count The least count (or vernier constant) of a vernier caliper is the minimum length it can measure accurately. It is calculated by dividing the value of the smallest division on the main scale by the total number of divisions on the vernier scale.

Least Count = Smallest division on main scaleTotal number of divisions on vernier scale

Example from the text: If the smallest main scale division is 1 mm and the vernier scale has 10 divisions, then: Least Count = 1 mm10 = 0.1 mm

• Out side jaws: Used for measuring external dimensions (like the diameter of a ball).
• Inside jaws: Used for measuring internal dimensions (like the inner diameter of a pipe).
• Retainer: A screw to hold the sliding scale in place.
• Main scale: The fixed scale.
• Vernier scale: The sliding scale.
• Depth probe: Used to measure the depth of a hole or container.

Detailed Explanation

The vernier caliper works on the principle of comparison between two scales. The main scale is like a regular ruler, with divisions of 1 mm. The vernier scale, which slides along the main scale, has divisions that are slightly smaller than those on the main scale. For example, 10 divisions on the vernier scale might cover a length of 9 mm on the main scale. This means each vernier division is 0.9 mm long.

• Close the jaws on the object to be measured.
• Read the main scale value just before the zero of the vernier scale.
• Find the division on the vernier scale that coincides exactly with any division on the main scale.
• Multiply this coinciding vernier division number by the least count.
• Add this value to the main scale reading to get the final measurement.

Total Reading = Main Scale Reading + (Vernier Scale Division × Least Count)

• (a) No zero error: The zero of the vernier scale coincides with the zero of the main scale.
• (b) Positive zero error: The zero of the vernier scale is to the right of the zero of the main scale.
• (c) Negative zero error: The zero of the vernier scale is to the left of the zero of the main scale.

The correction of zero error is a practical skill learned in laboratory work.

Intermediate Level

The vernier caliper is a crucial tool in any physics lab because it allows for precise measurements that are impossible with simpler tools. The key to its precision is the vernier scale. By carefully aligning the scale divisions, you can determine exactly how much of a main scale division the object's length exceeds. This is known as the vernier principle. For example, if you are measuring the diameter of a small cylinder, you can read the main scale to get the value in millimetres, and then use the vernier scale to find the fraction of a millimetre. This makes the vernier caliper an indispensable instrument for measuring small objects with high accuracy.

Important Points

• - The vernier caliper is used to measure lengths smaller than 1 mm.
• - It has two scales: a fixed main scale and a sliding vernier scale.
• - The least count is the smallest measurement it can make, usually 0.1 mm.
• - It can measure external dimensions (outside jaws), internal dimensions (inside jaws), and depth (depth probe).
• - Zero error must be checked and corrected before taking measurements.

Remember

• - Vernier Caliper: Measures fractions of a millimetre.
• - Least Count: Smallest measurement (e.g., 0.1 mm).
• - Least Count Formula: LC = Smallest main scale divisionTotal vernier scale divisions.
• - Two Scales: Main scale (fixed) and Vernier scale (sliding).

Common Mistakes

• - Forgetting to check for zero error: Always close the jaws and check if the zeros align. If not, you must apply a correction to your final reading.
• - Reading the wrong scale: Make sure you are reading the main scale correctly and then finding the correct coinciding vernier division.
• - Not using the correct jaws: Use the outside jaws for external dimensions and the inside jaws for internal dimensions. Using the wrong jaws will give an incorrect measurement.

Quick Revision

The vernier caliper is a precision measuring instrument used to measure lengths smaller than 1 mm. It has a fixed main scale and a sliding vernier scale. The least count, which is the smallest measurement the instrument can make, is calculated by dividing the smallest main scale division by the number of divisions on the vernier scale. A typical least count is 0.1 mm. It is used to measure internal and external dimensions, as well as depth.

60-Second Revision

The vernier caliper measures lengths to a fraction of a millimetre (e.g., 0.1 mm). It has a main scale and a sliding vernier scale. The least count is the smallest measurement it can make and is calculated as LC = Smallest main scale divisionTotal vernier scale divisions. Always check for zero error before measuring.

Frequently Asked Questions (FAQs)

Q1. What is a vernier caliper used for? Answer: A vernier caliper is a precision measuring instrument used to measure the thickness, diameter, or width of an object, as well as the internal and external diameter of a hollow cylinder. It is used to measure lengths smaller than 1 mm.

Q2. What is the least count of a vernier caliper? Answer: The least count is the minimum length that can be measured accurately with the instrument. It is calculated by dividing the smallest division on the main scale by the total number of divisions on the vernier scale. A typical least count is 0.1 mm.

Q3. How is the least count of a vernier caliper calculated? Answer: The formula is: Least Count = Smallest division on main scaleTotal number of divisions on vernier scale For example, if the smallest main scale division is 1 mm and the vernier scale has 10 divisions, then the least count is 1 mm10 = 0.1 mm.

Q4. What is zero error in a vernier caliper? Answer: Zero error is an error that occurs when the zero of the vernier scale does not coincide with the zero of the main scale when the jaws are closed. It can be positive or negative and must be corrected to get accurate measurements.

• Main scale: A fixed scale with markings.
• Vernier scale: A sliding scale.
• Out side jaws: For measuring external dimensions.
• Inside jaws: For measuring internal dimensions.
• Depth probe: For measuring depth.
• Retainer: To lock the sliding scale.

Q6. What is the difference between the main scale and the vernier scale? Answer: The main scale is a fixed scale with regular divisions, typically 1 mm. The vernier scale is a smaller, sliding scale that has markings that are slightly smaller than those on the main scale. The difference between the two scales allows for the measurement of fractions of the main scale division.

Multiple Choice Questions (MCQs)

• Q1. A vernier caliper is used to measure lengths smaller than:
• A. 1 cm
• B. 1 mm
• C. 1 m
• D. 1 μm

• Correct Answer: B
• Explanation: The text states that a vernier caliper can help take readings smaller than a millimetre.

• Q2. What is the formula for the least count of a vernier caliper?
• A. LC = Total vernier divisionsSmallest main scale division
• B. LC = Smallest main scale division × Total vernier divisions
• C. LC = Smallest main scale divisionTotal vernier scale divisions
• D. LC = Smallest main scale division + Total vernier divisions

• Correct Answer: C
• Explanation: The text defines the least count as the smallest division on the main scale divided by the total number of divisions on the vernier scale.

• Q3. If the smallest main scale division is 1 mm and the vernier scale has 10 divisions, the least count is:
• A. 0.01 mm
• B. 0.1 mm
• C. 1 mm
• D. 10 mm

• Correct Answer: B
• Explanation: LC = 1 mm10 = 0.1 mm.

• Q4. Which part of the vernier caliper is used to measure the internal diameter of a hollow cylinder?
• A. Outside jaws
• B. Inside jaws
• C. Depth probe
• D. Retainer

• Correct Answer: B
• Explanation: The text states that the inside jaws are used to measure the internal diameter of hollow cylinders.

• Q5. Zero error occurs when:
• A. The main scale is broken
• B. The vernier scale is broken
• C. The zeros of the two scales do not coincide when the jaws are closed
• D. The least count is too small

• Correct Answer: C
• Explanation: The text states that if the zeros do not coincide when the jaws are closed, there is an error called zero error.

• Q6. When the zero of the vernier scale is to the right of the zero of the main scale, the zero error is:
• A. Zero
• B. Positive
• C. Negative
• D. Infinite

• Correct Answer: B
• Explanation: Figure 1.9 in the text shows that a vernier scale zero to the right of the main scale zero is a positive zero error.

• Q7. A vernier caliper can be used to measure:
• A. Only external dimensions
• B. Only internal dimensions
• C. Only depth
• D. External dimensions, internal dimensions, and depth

• Correct Answer: D
• Explanation: The text lists all three uses: measuring thickness/diameter/width (external), internal diameter, and depth (using the depth probe).

• Q8. The main scale of a vernier caliper is:
• A. Sliding
• B. Fixed
• C. Flexible
• D. Digital

• Correct Answer: B
• Explanation: The text describes the main scale as fixed and the vernier scale as the sliding one.

• Q9. The retainer on a vernier caliper is used to:
• A. Measure depth
• B. Lock the sliding scale
• C. Measure internal diameter
• D. Measure external diameter

• Correct Answer: B
• Explanation: The text's diagram shows the retainer, which is a screw used to hold the sliding vernier scale in place.

• Q10. A length measured by a vernier caliper is 20.14 cm. What is the least count of the instrument?
• A. 1 cm
• B. 0.1 cm
• C. 0.01 cm
• D. 0.001 cm

Correct Answer: C Explanation: The reading has two decimal places, with the last digit (4) being the most uncertain. Since the reading is in cm, the least count is 0.01 cm (which is 0.1 mm).

Frequently Asked Questions (FAQs)

Q1. What is the difference between the main scale and the vernier scale? Answer: The main scale is a fixed, regular scale (like a ruler) with divisions of 1 mm. The vernier scale is a small, sliding scale with divisions that are slightly smaller than the main scale's divisions. The difference between the two allows for measurement of fractions of a millimetre.

• Read the main scale value just before the vernier zero.
• Find the vernier scale division that lines up exactly with a main scale division.
• Multiply this vernier division number by the least count.
• Add this value to the main scale reading to get the total measurement.

• Q3. What is the least count of a typical vernier caliper?
• Answer: The least count of a typical vernier caliper is 0.1 mm (or 0.01 cm).

Q4. What is a zero error, and how is it corrected? Answer: Zero error occurs when the instrument's zero is not at the true zero point when the jaws are closed. It can be positive or negative. To correct for it, you must determine the zero error value and then add or subtract it from your reading as appropriate. This is a standard procedure in laboratory work.

Q5. Can a vernier caliper measure the depth of a container? Answer: Yes. A vernier caliper has a depth probe (a thin rod that extends from the end of the main scale) that can be used to measure the depth of a hole or container.

Q6. What is the main advantage of a vernier caliper over a metre rule? Answer: A vernier caliper has a much smaller least count (0.1 mm vs. 1 mm for a metre rule). This means it is a much more precise instrument for measuring small lengths.

Multiple Choice Questions (MCQs)

• Q1. A vernier caliper is used to measure lengths smaller than:
• A. 1 cm
• B. 1 mm
• C. 1 m
• D. 1 μm

• Correct Answer: B
• Explanation: The text states that a vernier caliper can help take readings smaller than a millimetre.

• Q2. What is the formula for the least count of a vernier caliper?
• A. LC = Total vernier divisionsSmallest main scale division
• B. LC = Smallest main scale division × Total vernier divisions
• C. LC = Smallest main scale divisionTotal vernier scale divisions
• D. LC = Smallest main scale division + Total vernier divisions

• Correct Answer: C
• Explanation: The text defines the least count as the smallest division on the main scale divided by the total number of divisions on the vernier scale.

• Q3. If the smallest main scale division is 1 mm and the vernier scale has 10 divisions, the least count is:
• A. 0.01 mm
• B. 0.1 mm
• C. 1 mm
• D. 10 mm

• Correct Answer: B
• Explanation: LC = 1 mm10 = 0.1 mm.

• Q4. Which part of the vernier caliper is used to measure the internal diameter of a hollow cylinder?
• A. Outside jaws
• B. Inside jaws
• C. Depth probe
• D. Retainer

• Correct Answer: B
• Explanation: The text states that the inside jaws are used to measure the internal diameter of hollow cylinders.

• Q5. Zero error occurs when:
• A. The main scale is broken
• B. The vernier scale is broken
• C. The zeros of the two scales do not coincide when the jaws are closed
• D. The least count is too small

• Correct Answer: C
• Explanation: The text states that if the zeros do not coincide when the jaws are closed, there is an error called zero error.

• Q6. When the zero of the vernier scale is to the right of the zero of the main scale, the zero error is:
• A. Zero
• B. Positive
• C. Negative
• D. Infinite

• Correct Answer: B
• Explanation: Figure 1.9 in the text shows that a vernier scale zero to the right of the main scale zero is a positive zero error.

• Q7. A vernier caliper can be used to measure:
• A. Only external dimensions
• B. Only internal dimensions
• C. Only depth
• D. External dimensions, internal dimensions, and depth

• Correct Answer: D
• Explanation: The text lists all three uses: measuring thickness/diameter/width (external), internal diameter, and depth (using the depth probe).

• Q8. The main scale of a vernier caliper is:
• A. Sliding
• B. Fixed
• C. Flexible
• D. Digital

• Correct Answer: B
• Explanation: The text describes the main scale as fixed and the vernier scale as the sliding one.

• Q9. The retainer on a vernier caliper is used to:
• A. Measure depth
• B. Lock the sliding scale
• C. Measure internal diameter
• D. Measure external diameter

• Correct Answer: B
• Explanation: The text's diagram shows the retainer, which is a screw used to hold the sliding vernier scale in place.

• Q10. A length measured by a vernier caliper is 20.14 cm. What is the least count of the instrument?
• A. 1 cm
• B. 0.1 cm
• C. 0.01 cm
• D. 0.001 cm

Correct Answer: C Explanation: The reading has two decimal places, with the last digit (4) being the most uncertain. Since the reading is in cm, the least count is 0.01 cm (which is 0.1 mm).

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