Class 11 Physics Notes Chapter 2 (Chapter 2) – Lab Manual (English) Book

Detailed Notes with MCQs of a crucial tool you'll frequently encounter in the lab and in measurement-based problems: the Screw Gauge (or Micrometer Screw Gauge). This corresponds to the typical second experiment in your Class 11 Physics Lab Manual. Mastering this is essential, not just for practicals, but also because questions based on its principle and calculations often appear in competitive government exams.

Here are the detailed notes:

Experiment 2: To measure the diameter of a given wire / thickness of a given sheet using a screw gauge.

1. Aim:
To determine the diameter of a given wire (or thickness of a sheet) using a screw gauge and calculate its cross-sectional area (if required).

2. Apparatus:
Screw gauge, the given wire (or sheet), magnifying glass (optional), pencil, and lab notebook.

3. Principle/Theory:

• Working Principle: The screw gauge works on the principle of converting a small linear distance into a larger circular rotation using a screw mechanism. A known linear distance moved by the screw (pitch) corresponds to one complete rotation of the circular scale. This allows for very fine measurements.
• Pitch: The pitch of the screw gauge is the linear distance moved by the screw (along the main scale) when the circular (or thimble) scale completes one full rotation (360°).
  • Calculation: Pitch = (Distance moved by the screw) / (Number of full rotations given)
  • Commonly: Distance moved for 4 or 5 rotations is noted, and then the average pitch is calculated. For most standard screw gauges, the pitch is 1 mm or 0.5 mm.
• Least Count (LC): The least count is the smallest measurement that can be accurately made using the instrument. It represents the linear distance moved by the screw when the circular scale rotates by just one division.
  • Calculation: Least Count (LC) = Pitch / (Total number of divisions on the circular scale)
  • Example: If Pitch = 1 mm and Total divisions on circular scale = 100, then LC = 1 mm / 100 = 0.01 mm = 0.001 cm.
  • Example: If Pitch = 0.5 mm and Total divisions on circular scale = 50, then LC = 0.5 mm / 50 = 0.01 mm = 0.001 cm.
• Measurement Reading: The total reading is obtained by adding the Main Scale Reading (MSR) to the Circular Scale Reading (CSR).
  • Main Scale Reading (MSR): This is the reading on the linear (sleeve) scale just visible before the edge of the circular (thimble) scale. It's read in millimeters.
  • Circular Scale Division (CSD): This is the division on the circular scale that coincides with the baseline (reference line) of the main scale.
  • Circular Scale Reading (CSR): CSR = CSD × LC
  • Total Reading (Observed): TR = MSR + CSR = MSR + (CSD × LC)

4. Zero Error and Zero Correction:

• Before taking measurements, the zero error must be determined by bringing the flat end of the screw (spindle) in contact with the stud (anvil) without placing any object in between.
• No Zero Error: If the zero mark of the circular scale coincides perfectly with the baseline of the main scale, there is no zero error.
• Positive Zero Error (+ve): If the zero mark of the circular scale is below the baseline when the jaws are closed, the error is positive.
  • Identification: Note the circular scale division (n) coinciding with the baseline.
  • Calculation: Positive Zero Error = + (n × LC)
  • Correction: Zero Correction = - (n × LC). (Subtract the error from the observed reading).
• Negative Zero Error (-ve): If the zero mark of the circular scale is above the baseline when the jaws are closed, the error is negative.
  • Identification: Note the circular scale division (n') coinciding with the baseline. The actual division to use is (Total Circular Divisions - n'). Let this be 'm'. (e.g., if 95th division coincides on a 100-division scale, m = 100 - 95 = 5). Alternatively, some consider the reading directly as negative. Let's stick to the standard: find the coinciding division 'n'. The error is calculated based on how much short it is from the zero completing its round. If the 95th division coincides (on a 100 div scale), it means zero has gone 5 divisions past the reference line in the negative direction.
  • Calculation: Negative Zero Error = - [(Total Circular Divisions - n') × LC] = - (m x LC)
  • Correction: Zero Correction = + [(Total Circular Divisions - n') × LC] = + (m x LC). (Add the correction magnitude to the observed reading).
• Corrected Reading: Corrected Reading = Observed Reading - Zero Error = Observed Reading + Zero Correction.

5. Procedure (Brief Outline):

1. Determine the pitch of the screw gauge.
2. Determine the least count (LC) of the screw gauge.
3. Find the zero error (if any) and calculate the zero correction. Note its sign carefully.
4. Place the wire/sheet between the spindle and the anvil. Rotate the ratchet until a clicking sound is heard (ensures uniform pressure). Do not overtighten.
5. Note the Main Scale Reading (MSR).
6. Note the Circular Scale Division (CSD) coinciding with the baseline.
7. Calculate the Circular Scale Reading (CSR = CSD × LC).
8. Calculate the Observed Total Reading (TR = MSR + CSR).
9. Repeat steps 4-8 for different positions and orientations of the wire/sheet to get multiple readings (usually 3-5).
10. Calculate the average observed reading.
11. Apply the zero correction to the average observed reading to get the final corrected diameter/thickness.

6. Observations Table (Example Structure):

• Pitch = ______ mm
• Total divisions on circular scale = ______
• Least Count (LC) = ______ mm
• Zero Error = ______ mm
• Zero Correction = ______ mm

7. Calculations:

• Average Observed Diameter = (Sum of all observed diameters) / (Number of observations)
• Corrected Diameter = Average Observed Diameter + Zero Correction (Remember Zero Correction has the opposite sign to Zero Error).
• (If asked) Radius (r) = Corrected Diameter / 2
• (If asked) Cross-sectional Area (A) = πr²

8. Result:
The average corrected diameter of the given wire (or thickness of the sheet) is ______ mm = ______ cm.

9. Precautions:

1. Always rotate the screw using the ratchet arrangement to avoid undue pressure.
2. The screw gauge should be free from backlash error (check by rotating the screw in one direction and then reversing). If present, always rotate in the same direction while taking readings.
3. Check for zero error before starting the experiment.
4. Avoid parallax error while reading the scales. View the scales perpendicularly.
5. Take readings at multiple points and orientations on the object and average them.
6. Clean the faces of the anvil and spindle before use.
7. Ensure the object is held gently but firmly between the jaws.

10. Sources of Error:

1. Zero Error: Instrument may not read zero when jaws are closed.
2. Backlash Error: Due to wear and tear of screw threads, there might be a lag when the direction of rotation is reversed.
3. Parallax Error: Incorrect positioning of the eye while taking readings.
4. Non-uniformity: The wire/sheet may not have a uniform diameter/thickness.
5. Excessive Pressure: Applying too much pressure using the thimble (instead of ratchet) can damage the object or the instrument and lead to incorrect readings.
6. Dirt/Grease: Presence of dirt on anvil/spindle faces.

Relevance for Exams: Questions often test your understanding of Pitch, LC calculation, reading interpretation from diagrams, zero error identification and correction, and potential sources of error.

Multiple Choice Questions (MCQs):

1. The pitch of a screw gauge is 0.5 mm and there are 50 divisions on the circular scale. What is the least count of the screw gauge?
   (a) 0.001 mm
   (b) 0.01 mm
   (c) 0.1 mm
   (d) 0.05 mm

2. While measuring the diameter of a wire using a screw gauge, the Main Scale Reading (MSR) is 2 mm and the 45th division of the circular scale coincides with the baseline. If the least count is 0.01 mm, the observed diameter is:
   (a) 2.045 mm
   (b) 2.45 mm
   (c) 2.0045 mm
   (d) 4.7 mm

3. A screw gauge has a positive zero error of 5 divisions. If the LC is 0.01 mm, what is the zero correction?
   (a) +0.05 mm
   (b) -0.05 mm
   (c) +0.5 mm
   (d) -0.5 mm

4. If the zero mark of the circular scale is above the baseline by 3 divisions when the jaws are closed (on a 100 division scale with LC = 0.01 mm), the zero error is:
   (a) +0.03 mm
   (b) -0.03 mm
   (c) +0.97 mm
   (d) -0.97 mm

5. The ratchet in a screw gauge is used to:
   (a) Measure the pitch
   (b) Apply uniform pressure
   (c) Correct for zero error
   (d) Lock the spindle

6. The term 'backlash error' in a screw gauge is associated with:
   (a) Incorrect calibration of the main scale
   (b) Wear and tear of the screw threads
   (c) Parallax in reading the scale
   (d) Non-uniformity of the object being measured

7. A screw moves by 2 mm on the main scale for 4 complete rotations of the circular scale. The pitch of the screw is:
   (a) 2 mm
   (b) 8 mm
   (c) 0.5 mm
   (d) 0.25 mm

8. To measure the diameter of a thin wire most accurately, one should use:
   (a) A metre scale
   (b) Vernier callipers
   (c) A screw gauge
   (d) A spherometer

9. Consider a screw gauge with LC = 0.001 cm. The MSR is 0.3 cm and the CSD is 25. The observed reading is:
   (a) 0.325 cm
   (b) 0.55 cm
   (c) 0.3025 cm
   (d) 3.25 cm

10. When the flat end of the screw touches the stud of a screw gauge, the zero of the circular scale is below the baseline and the 8th division coincides with the baseline. If LC = 0.01 mm, the zero error is:
    (a) -0.08 mm
    (b) +0.08 mm
    (c) -0.92 mm
    (d) +0.92 mm

Answers to MCQs:

1. (b) 0.01 mm (LC = Pitch / No. of divisions = 0.5 mm / 50 = 0.01 mm)
2. (b) 2.45 mm (TR = MSR + CSD × LC = 2 mm + 45 × 0.01 mm = 2 + 0.45 = 2.45 mm)
3. (b) -0.05 mm (Zero Error = + (5 × 0.01 mm) = +0.05 mm. Zero Correction = - Zero Error = -0.05 mm)
4. (b) -0.03 mm (Zero mark above means negative error. Error = - (3 × 0.01 mm) = -0.03 mm. Alternatively, 100-3=97th division. Error = -(100-97)LC = -30.01 = -0.03mm)
5. (b) Apply uniform pressure
6. (b) Wear and tear of the screw threads
7. (c) 0.5 mm (Pitch = Distance / Rotations = 2 mm / 4 = 0.5 mm)
8. (c) A screw gauge (It has the highest precision among the choices for this type of measurement)
9. (a) 0.325 cm (TR = MSR + CSD × LC = 0.3 cm + 25 × 0.001 cm = 0.3 + 0.025 = 0.325 cm)
10. (b) +0.08 mm (Zero below baseline means positive error. Error = + (8 × 0.01 mm) = +0.08 mm)

Study these notes carefully, focusing on the definitions, formulas, and error analysis. Practice interpreting readings from diagrams if you find them in textbooks or online resources. Good luck!