Class 11 Physics Notes Chapter 4 (Chapter 4) – Lab Manual (English) Book

Detailed Notes with MCQs of Chapter 4 from your Physics Lab Manual. This chapter deals with two fundamental measuring instruments: the Vernier Callipers and the Screw Gauge. Mastering these is crucial, not just for your practical exams, but also because questions based on their principles, least count, and error calculations frequently appear in various government examinations.

Chapter 4: Vernier Callipers and Screw Gauge

1. Vernier Callipers

• Objective: To measure the length of an object, diameter of a sphere, diameter (internal and external) of a beaker/calorimeter, and depth of a beaker with accuracy greater than a standard meter scale.
• Principle: The Vernier Callipers works on the principle of using the difference between the sizes of one main scale division (MSD) and one vernier scale division (VSD) to measure the fraction of a main scale division accurately.
  • Usually, 'n' divisions on the Vernier Scale (VSD) coincide with '(n-1)' divisions on the Main Scale (MSD).
  • Therefore, n VSD = (n-1) MSD
  • Or, 1 VSD = (n-1)/n MSD
• Least Count (LC): The smallest measurement that can be accurately made using the instrument. It's also known as the Vernier Constant.
  • LC = Value of 1 Main Scale Division (MSD) - Value of 1 Vernier Scale Division (VSD)
  • LC = 1 MSD - [(n-1)/n] MSD
  • LC = [1 - (n-1)/n] MSD = [ (n - n + 1) / n ] MSD = (1/n) MSD
  • Common Formula: LC = (Value of 1 MSD) / (Total number of divisions on Vernier Scale)
  • Example: If 1 MSD = 1 mm and there are 10 divisions on the Vernier Scale, then LC = 1 mm / 10 = 0.1 mm = 0.01 cm.
• Reading a Measurement:
  • Main Scale Reading (MSR): Read the main scale mark just to the left of the zero mark of the vernier scale.
  • Vernier Scale Coincidence (VSC): Find the division on the vernier scale that exactly coincides with any division on the main scale. Let this be the 'p'-th division.
  • Total Reading = MSR + (VSC × LC)
• Zero Error and Zero Correction:
  • No Zero Error: If the zero mark of the Vernier scale coincides exactly with the zero mark of the main scale when the jaws are closed.
  • Positive Zero Error (+ve ZE): If the zero mark of the Vernier scale is to the right of the main scale zero when the jaws are closed.
    • Find the coinciding Vernier division (say 'x').
    • Positive Zero Error = + (x × LC)
    • Zero Correction (ZC) = - (x × LC)
  • Negative Zero Error (-ve ZE): If the zero mark of the Vernier scale is to the left of the main scale zero when the jaws are closed.
    • Find the coinciding Vernier division (say 'y').
    • Negative Zero Error = - [(Total Vernier Divisions - y) × LC]
    • Zero Correction (ZC) = + [(Total Vernier Divisions - y) × LC]
  • Corrected Reading = Observed Reading + Zero Correction (Remember: Correction is opposite in sign to the Error).

2. Screw Gauge

• Objective: To measure the diameter of a given wire, the thickness of a given sheet, or the diameter of small spherical objects with even greater precision than Vernier Callipers.
• Principle: It works on the principle of a screw. The linear distance moved by the screw is directly proportional to the amount of rotation given to its head.
• Pitch: The linear distance moved by the screw along the main scale when the circular scale completes one full rotation.
  • Pitch = (Distance moved by screw) / (Number of full rotations given)
  • Usually, 1 rotation moves the screw by 1 mm or 0.5 mm.
• Least Count (LC): The linear distance moved by the screw when the circular scale rotates by just one division.
  • LC = Pitch / (Total number of divisions on the Circular Scale)
  • Example: If Pitch = 1 mm and there are 100 divisions on the circular scale, LC = 1 mm / 100 = 0.01 mm = 0.001 cm.
• Reading a Measurement:
  • Main Scale Reading (MSR) / Linear Scale Reading (LSR): Read the marking on the main scale (sleeve) that is fully visible just before the edge of the circular scale (thimble).
  • Circular Scale Reading (CSR): Read the division on the circular scale that coincides with the baseline (reference line) of the main scale. Let this be the 'q'-th division.
  • Total Reading = MSR + (CSR × LC)
• Zero Error and Zero Correction:
  • No Zero Error: If the zero mark of the circular scale coincides exactly with the baseline of the main scale when the stud and spindle touch.
  • Positive Zero Error (+ve ZE): If the zero mark of the circular scale is below the baseline when the stud and spindle touch.
    • Find the coinciding circular scale division (say 'a').
    • Positive Zero Error = + (a × LC)
    • Zero Correction (ZC) = - (a × LC)
  • Negative Zero Error (-ve ZE): If the zero mark of the circular scale is above the baseline when the stud and spindle touch.
    • Note the circular scale division coinciding with the baseline (say 'b'). Often, you read the number of divisions below the baseline to reach 100 (or total divisions). Let this be 'b' directly or (Total divisions - division reading).
    • Negative Zero Error = - [(Total Circular Divisions - b) × LC] (where 'b' is the division coinciding with the baseline)
    • Zero Correction (ZC) = + [(Total Circular Divisions - b) × LC]
  • Corrected Reading = Observed Reading + Zero Correction

Key Points for Exams:

• Understand the difference in precision (LC) between a meter scale, Vernier Callipers, and Screw Gauge.
• Be able to calculate LC for both instruments given the necessary parameters (MSD, VSD count, Pitch, Circular scale divisions).
• Be able to calculate the observed reading from given MSR, VSC/CSR, and LC.
• Crucially, understand how to identify positive and negative zero errors from diagrams or descriptions and calculate the error and correction.
• Know how to apply the zero correction to find the true measurement.
• Remember the units (mm or cm) and be consistent.
• Precautions like avoiding parallax error, backlash error (in screw gauge), and applying gentle & uniform pressure are important conceptually.

Multiple Choice Questions (MCQs)

1. In a Vernier Callipers, 10 Vernier Scale Divisions (VSD) coincide with 9 Main Scale Divisions (MSD). If 1 MSD is 1 mm, the Least Count of the instrument is:
   a) 1 mm
   b) 0.1 mm
   c) 0.01 mm
   d) 0.9 mm

2. While measuring the diameter of a sphere using Vernier Callipers, the Main Scale Reading (MSR) is 2.4 cm and the 6th Vernier Scale Division coincides with a main scale division. If the Least Count is 0.01 cm, the observed diameter is:
   a) 2.406 cm
   b) 2.46 cm
   c) 2.40 cm
   d) 3.0 cm

3. A student observes that the zero of the Vernier scale is to the right of the zero of the main scale when the jaws are closed. The 4th VSD coincides with an MSD. If LC = 0.01 cm, the Zero Error is:
   a) +0.04 cm
   b) -0.04 cm
   c) +0.06 cm
   d) -0.06 cm

4. The pitch of a screw gauge is 0.5 mm and there are 50 divisions on the circular scale. The Least Count of the screw gauge is:
   a) 0.01 mm
   b) 0.001 mm
   c) 0.1 mm
   d) 0.05 mm

5. In a screw gauge measurement, the Main Scale Reading (MSR) is 3 mm and the 25th division of the circular scale coincides with the baseline. If the Least Count is 0.01 mm, the observed reading is:
   a) 3.25 mm
   b) 3.025 mm
   c) 5.5 mm
   d) 3.0 mm

6. When the spindle and stud of a screw gauge touch, the zero of the circular scale is 5 divisions below the baseline. If LC = 0.01 mm, the Zero Correction is:
   a) +0.05 mm
   b) -0.05 mm
   c) +0.005 mm
   d) -0.005 mm

7. When the spindle and stud of a screw gauge (with 100 circular divisions) touch, the zero of the circular scale is above the baseline, and the 92nd division coincides with the baseline. If LC = 0.01 mm, the Zero Error is:
   a) +0.92 mm
   b) -0.92 mm
   c) +0.08 mm
   d) -0.08 mm

8. The least count of a measuring instrument signifies its:
   a) Range
   b) Accuracy
   c) Precision
   d) Zero error

9. To measure the internal diameter of a hollow cylinder using Vernier Callipers, which part of the instrument is used?
   a) Lower jaws
   b) Upper jaws
   c) Strip at the back
   d) Main scale only

10. Backlash error is commonly associated with which instrument?
    a) Meter Scale
    b) Vernier Callipers
    c) Screw Gauge
    d) Stop Watch

Answers to MCQs:

1. b) 0.1 mm (LC = 1 MSD / 10 = 1 mm / 10 = 0.1 mm)
2. b) 2.46 cm (Reading = MSR + VSC * LC = 2.4 cm + 6 * 0.01 cm = 2.4 + 0.06 = 2.46 cm)
3. a) +0.04 cm (Zero right -> Positive error. ZE = + VSC * LC = + 4 * 0.01 cm = +0.04 cm)
4. a) 0.01 mm (LC = Pitch / No. of divisions = 0.5 mm / 50 = 0.01 mm)
5. a) 3.25 mm (Reading = MSR + CSR * LC = 3 mm + 25 * 0.01 mm = 3 + 0.25 = 3.25 mm)
6. b) -0.05 mm (Zero below -> Positive error. ZE = + 5 * LC = + 5 * 0.01 mm = +0.05 mm. Correction = -ZE = -0.05 mm)
7. d) -0.08 mm (Zero above -> Negative error. Coinciding division = 92. Error = - (100 - 92) * LC = - 8 * 0.01 mm = -0.08 mm)
8. c) Precision (Least count refers to the smallest value that can be measured, indicating the resolution or precision)
9. b) Upper jaws (The smaller, upper jaws are designed to fit inside objects)
10. c) Screw Gauge (Due to wear and tear in the screw mechanism)

Study these concepts thoroughly. Pay close attention to the calculation of Least Count and the identification and correction of Zero Errors. Good luck with your preparation!