Theory: Vernier Callipers & Measurements
1. Vernier Principle
A vernier calliper has a main scale (MSD = 1 mm) and a vernier scale that slides over it. The vernier scale has N divisions, each slightly shorter than 1 MSD. The "mismatch" between scales gives precision beyond what the eye can see. The key insight: when the nth vernier division aligns with ANY main scale mark, the extra length measured = n × LC.
2. Least Count Formula
LC = 1 MSD − 1 VSD
LC = MSD value / N (when N VSD = (N−1) MSD, standard case)
📌 Standard vernier: 10 VSD = 9 MSD → LC = 0.1 mm
📌 This problem: 20 VSD = 16 MSD → LC = 0.2 mm
📌 50-division vernier: 50 VSD = 49 MSD → LC = 0.02 mm
📌 Smaller LC = more precise instrument
3. Reading a Vernier Calliper
Total reading = Main scale reading + (coinciding vernier division × LC). If MSR = 23 mm and 8th VSD coincides: Reading = 23 + (8 × 0.2) = 23 + 1.6 = 24.6 mm. The coinciding vernier division is found by looking at which VSD mark lines up perfectly with any MSD mark.
4. Zero Error
Zero error = reading when jaws are fully closed. Positive zero error (vernier zero right of main zero) → subtract from observed. Negative zero error (vernier zero left of main zero) → add to observed. Corrected reading = Observed − Zero error.
5. Screw Gauge Comparison
📌 Vernier LC = 0.1 mm (standard) — for lengths, diameters
📌 Screw gauge LC = 0.01 mm — for thin wires, plates
📌 LC of screw gauge = Pitch / No. of circular divisions
📌 Common screw gauge: pitch = 0.5 mm, 50 div → LC = 0.01 mm
⚠️ 20 VSD = 16 MSD → 1 VSD = 16/20 (not 20/16) MSD
⚠️ LC = 1 MSD − 1 VSD = 1 − 0.8 = 0.2 mm (not 0.1)
⚠️ 0.2 mm = 0.02 cm — both options 1 and 3 are same value!
Frequently Asked Questions
1. What is 1 VSD in this problem? ⌄
20 VSD = 16 MSD → 1 VSD = 16/20 = 0.8 MSD = 0.8 mm. So each vernier division is 0.8 mm, which is 0.2 mm less than 1 MSD (1 mm). This 0.2 mm difference is the least count.
2. Are options 1 and 3 both correct? ⌄
Mathematically yes — 0.2 mm = 0.02 cm. But option 2 says 0.01 cm = 0.1 mm which is WRONG. Option 4 says 0.1 mm which is also WRONG. Options 1 and 3 express the same value. In NEET, option 1 would be marked correct.
3. What is LC of standard vernier calliper? ⌄
Standard: 10 VSD = 9 MSD. 1 VSD = 0.9 mm. LC = 1 − 0.9 = 0.1 mm = 0.01 cm. This is the most common vernier used in NEET practical questions. Memorise: standard vernier LC = 0.1 mm.
4. How is LC of screw gauge calculated? ⌄
LC = Pitch / N. Pitch = distance moved per rotation. For pitch = 1 mm, 100 divisions: LC = 1/100 = 0.01 mm. For pitch = 0.5 mm, 50 divisions: LC = 0.5/50 = 0.01 mm. Both common screw gauges give LC = 0.01 mm.
5. What is backlash error in screw gauge? ⌄
Backlash error occurs due to loose fitting between screw threads — when direction of rotation is reversed, the screw moves slightly before engaging. To avoid: always approach the final position by turning in the same direction. Never reverse direction while taking a reading.
6. If main scale reads 12 mm and 6th vernier division coincides, what is the reading? ⌄
Reading = MSR + (n × LC) = 12 + (6 × 0.2) = 12 + 1.2 = 13.2 mm. The vernier adds the fractional mm that the main scale cannot resolve. This is the fundamental principle of the vernier calliper.
7. What does "precision" mean in measurement? ⌄
Precision = the smallest unit of measurement the instrument can make = least count. A vernier with LC = 0.1 mm is more precise than one with LC = 0.2 mm. Precision is NOT the same as accuracy — accuracy refers to how close a measurement is to the true value.
8. Why do vernier scales have a different number of divisions? ⌄
The vernier works because its divisions are slightly different in size from main scale divisions. This creates a "beat" pattern where different vernier lines come into alignment at different positions, allowing sub-division of the main scale. More vernier divisions → finer subdivision → smaller LC.