- Dr.Sanjaykumar Pawar
 |
| Comparison of measuring instruments showing how least count affects precision in Physics for NEET preparation. |
CBSE Class 11 Physics Notes
Chapter: Units and Measurements
Question
Which of the following is the most precise device for measuring length?
(a) A vernier callipers with 20 divisions on the sliding scale.
(b) A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
(c) An optical instrument that can measure length to within a wavelength of light.
Step-by-Step Solution
Step 1: Find the Least Count of Vernier Callipers
20 Vernier Scale Divisions = 19 Main Scale Divisions
Least Count = 1 MSD − 1 VSD
LC = 1/20 mm
Least Count = 0.05 mm
Step 2: Find the Least Count of Screw Gauge
Given:
- Pitch = 1 mm
- Circular Scale Divisions = 100
Least Count = Pitch ÷ Number of Circular Scale Divisions
LC = 1 ÷ 100
Least Count = 0.01 mm
Step 3: Optical Instrument
Optical instruments measure length up to one wavelength of light.
Average wavelength of visible light
λ ≈ 5 × 10-7 m
≈ 0.0005 mm
≈ 0.0005 mm
Therefore, Least Count ≈ 0.0005 mm
Step 4: Comparison
| Instrument | Least Count |
|---|---|
| Vernier Callipers | 0.05 mm |
| Screw Gauge | 0.01 mm |
| Optical Instrument | 0.0005 mm |
Smaller Least Count = Greater Precision
0.0005 mm is the smallest.
Correct Answer: (c) Optical Instrument
0.0005 mm is the smallest.
Correct Answer: (c) Optical Instrument
Complete Notes
1. Measurement
Measurement means comparing an unknown quantity with a standard quantity.
Examples
- Measuring length using a ruler.
- Measuring wire diameter using a screw gauge.
- Measuring pipe diameter using a vernier callipers.
2. Least Count
Least Count is the smallest value that an instrument can measure accurately.
Smaller Least Count = Higher Precision
3. Accuracy
Accuracy means how close a measured value is to the true value.
Example: Actual length = 10.00 cm Measured length = 10.01 cm This is highly accurate.
4. Precision
Precision means how close repeated measurements are to each other.
Example
- 10.02 cm
- 10.01 cm
- 10.02 cm
- 10.01 cm
These readings are highly precise.
5. Difference Between Accuracy and Precision
| Accuracy | Precision |
|---|---|
| Close to true value | Close to repeated values |
| Correctness | Repeatability |
6. Vernier Callipers
Uses
- External diameter
- Internal diameter
- Depth
Least Count = 1 MSD − 1 VSD
For 20 divisions, LC = 0.05 mm
7. Screw Gauge
Uses
- Diameter of wire
- Thickness of paper
- Metal sheet thickness
Pitch = Distance moved in one complete rotation.
Least Count = Pitch ÷ Circular Scale Divisions
Example
Pitch = 1 mm
Divisions = 100
LC = 0.01 mm
8. Optical Instrument
Uses light waves to measure extremely small distances.
Approximate precision
0.0005 mm
This is the most precise among the given instruments.
9. Comparison of Measuring Instruments
| Instrument | Least Count | Precision |
|---|---|---|
| Metre Scale | 1 mm | Low |
| Vernier Callipers | 0.05 mm | Better |
| Screw Gauge | 0.01 mm | Very Good |
| Optical Instrument | 0.0005 mm | Highest |
Important Formulas
Least Count (Screw Gauge)
LC = Pitch ÷ Number of Circular Scale Divisions
LC = Pitch ÷ Number of Circular Scale Divisions
Least Count (Vernier Callipers)
LC = 1 MSD − 1 VSD
LC = 1 MSD − 1 VSD
Quick Revision
- Measurement compares an unknown quantity with a standard.
- Least Count = Smallest measurable value.
- Smaller Least Count means Higher Precision.
- Accuracy = Closeness to true value.
- Precision = Closeness of repeated readings.
- Vernier Callipers LC = 0.05 mm.
- Screw Gauge LC = 0.01 mm.
- Optical Instrument LC ≈ 0.0005 mm.
- Most Precise Instrument = Optical Instrument.
Exam Tip:
Whenever you are asked to compare measuring instruments, always compare their least counts. The instrument with the smallest least count is the most precise.
Whenever you are asked to compare measuring instruments, always compare their least counts. The instrument with the smallest least count is the most precise.
NEET Smart Learning Structure
Topic: Precision of Measuring Instruments
1. Exam Snapshot (30 Seconds Rule)
✔ Least Count जितना कम होगा → Precision उतनी अधिक होगी
Order:
Metre Scale → Vernier Callipers → Screw Gauge → Optical Instrument
Order:
Metre Scale → Vernier Callipers → Screw Gauge → Optical Instrument
2. Visual Memory Table
| Instrument | Least Count | Precision | Uses | NEET Keyword |
|---|---|---|---|---|
| Metre Scale | 1 mm | Low | Basic length | Easy |
| Vernier Callipers | 0.05 mm | Better | Diameter, Depth | Medium |
| Screw Gauge | 0.01 mm | High | Wire thickness | Important |
| Optical Instrument | 0.0005 mm | Highest | Atomic level | Advanced |
3. Memory Trick (Mnemonic)
Mnemonic: "मेरा वीर शेर ऑपरेशन करेगा"
म = Metre Scale
वीर = Vernier Callipers
शेर = Screw Gauge
ऑपरेशन = Optical Instrument
म = Metre Scale
वीर = Vernier Callipers
शेर = Screw Gauge
ऑपरेशन = Optical Instrument
✔ Top to Bottom: Least Count ↓, Precision ↑
4. Golden Rule
⭐ सबसे छोटा Least Count = सबसे अधिक Precision
5. Formula Box
Vernier Callipers:
LC = 1 MSD − 1 VSD
Screw Gauge:
LC = Pitch / Circular Scale Division
LC = 1 MSD − 1 VSD
Screw Gauge:
LC = Pitch / Circular Scale Division
6. Concept Tree
Measurement → Instrument → Least Count → Precision → Comparison → MCQ → NEET Trick
7. Flow Chart
Measurement → Least Count → Smaller LC → Higher Precision → Correct Answer
8. Common Mistakes
❌ Accuracy और Precision को एक समझ लेना
❌ Larger Least Count को ज्यादा Precision समझ लेना
❌ Formula भूल जाना
❌ Larger Least Count को ज्यादा Precision समझ लेना
❌ Formula भूल जाना
9. NEET Trick
Question में सभी instruments की Least Count compare करो
✔ सबसे छोटा LC → Correct Answer
✔ सबसे छोटा LC → Correct Answer
10. PYQ Strategy
Step 1: Instrument पहचानो
Step 2: Least Count निकालो
Step 3: Compare करो
Step 4: Smallest LC चुनो
Step 2: Least Count निकालो
Step 3: Compare करो
Step 4: Smallest LC चुनो
11. One Page Revision
Measurement → Least Count → Accuracy → Precision → Vernier → Screw Gauge → Optical → Smallest LC = Best
12. 15 Second Revision
Least Count छोटा → Precision बड़ा → Optical Best → Answer (C)
13. Sample MCQ
Q: सबसे अधिक precise instrument कौन है?
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Answer: D
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Answer: D
14. Assertion Reason
Assertion: Optical instrument सबसे precise है
Reason: इसका least count सबसे कम है
Answer: Both true and correct explanation
Reason: इसका least count सबसे कम है
Answer: Both true and correct explanation
15. Final Memory Map
Measurement → Least Count → Precision → Comparison → Trick → MCQ → Revision
Golden Formula
Smallest Least Count = Highest Precision = Correct Answer
NEET Practice Questions
Topic: Precision, Least Count, Measuring Instruments
1. Direct MCQs (Single Correct Option)
Q1 (Easy)
Which instrument has the smallest least count?
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Which instrument has the smallest least count?
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Answer: D (Optical Instrument)
Q2 (Easy)
Least count is defined as:
A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement
Least count is defined as:
A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement
Answer: B
Q3 (Moderate)
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:
A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:
A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm
Answer: C
Q4 (Hard)
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:
A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:
A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm
Answer: B
2. Statement-Based Questions
Q5
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.
A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.
A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true
Answer: A
Q6
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.
A) Both true
B) I true II false
C) I false II true
D) Both false
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.
A) Both true
B) I true II false
C) I false II true
D) Both false
Answer: B
3. Assertion and Reason (A & R)
Q7
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.
A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.
A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true
Answer: A
Q8
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.
A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.
A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true
Answer: A
4. Match the Columns
Q9
Match Column I with Column II:
Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument
Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm
Match Column I with Column II:
Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument
Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm
Answer:
1 → B
2 → C
3 → D
4 → A
1 → B
2 → C
3 → D
4 → A
5. Diagram / Graph-Based Questions
Q10
A graph shows comparison of least count of instruments:
Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)
Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise
A graph shows comparison of least count of instruments:
Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)
Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise
Answer: C
Q11
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero
Answer: B
Final NEET Shortcut Rule
✔ Least Count ↓ → Precision ↑
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision
NEET Practice Questions
Topic: Precision, Least Count, Measuring Instruments
1. Direct MCQs (Single Correct Option)
Q1 (Easy)
Which instrument has the smallest least count?
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Which instrument has the smallest least count?
A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument
Answer: D (Optical Instrument)
Q2 (Easy)
Least count is defined as:
A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement
Least count is defined as:
A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement
Answer: B
Q3 (Moderate)
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:
A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:
A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm
Answer: C
Q4 (Hard)
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:
A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:
A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm
Answer: B
2. Statement-Based Questions
Q5
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.
A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.
A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true
Answer: A
Q6
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.
A) Both true
B) I true II false
C) I false II true
D) Both false
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.
A) Both true
B) I true II false
C) I false II true
D) Both false
Answer: B
3. Assertion and Reason (A & R)
Q7
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.
A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.
A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true
Answer: A
Q8
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.
A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.
A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true
Answer: A
4. Match the Columns
Q9
Match Column I with Column II:
Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument
Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm
Match Column I with Column II:
Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument
Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm
Answer:
1 → B
2 → C
3 → D
4 → A
1 → B
2 → C
3 → D
4 → A
5. Diagram / Graph-Based Questions
Q10
A graph shows comparison of least count of instruments:
Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)
Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise
A graph shows comparison of least count of instruments:
Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)
Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise
Answer: C
Q11
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero
Answer: B
Final NEET Shortcut Rule
✔ Least Count ↓ → Precision ↑
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision
🔗 11. Internal Links
/neet-physics-measurement-basics
/least-count-vernier-callipers-explained
/screw-gauge-formula-and-examples
/optical-instruments-physics-neet
/physics-mcqs-class-11-chapter-1
/assertion-reason-questions-physics
/neet-short-tricks-physics
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