IITJEE: Vernier Callipers Screw Gauge Interactive

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APEX CLASS • IITJEE Experimental Physics Lab

Vernier Callipers & Screw Gauge Interactive Simulator

Master Least Count, Positive/Negative Zero Error, and Coincidence Readings with one tap!

🔍 Tap a Vernier Calliper Position to Inspect Scale Alignment:
MAIN SCALE (1 MSD = 1.0 mm) 0 5mm 10mm (1cm) 15mm 20mm (2cm) Sphere = 12.6 mm VERNIER SCALE (10 VSD = 9 MSD) 0 1234 5 6789 10 ✅ Perfect Zero: Vernier 0 aligns exactly with Main Scale 0 (Zero Error = 0.0 mm) ⚠️ POSITIVE ZERO ERROR: Vernier 0 is RIGHT of Main 0, and 3rd VSD coincides → Z.E. = +0.3 mm (Subtract it!) ❄️ NEGATIVE ZERO ERROR: Vernier 0 is LEFT of Main 0 & 6th VSD coincides → -(10 – 6)×0.1 = -0.4 mm (Add it!) 🎯 6th Vernier Division Coincides! Reading = 12 mm (MSR) + 6 × 0.1 mm = 12.6 mm
Least Count (LC) Formula
1 MSD – 1 VSD = 0.1 mm
1 mm – (9/10) mm = 0.01 cm
Main Scale Reading (MSR)
0.0 mm 0.0 mm (Jaws Closed) 0.0 mm (Jaws Closed) 12.0 mm (Mark before 0)
Read just left of Vernier Zero
Vernier Coincidence (VSR)
0 × 0.1 = 0.0 mm 3rd line → +0.3 mm 6th line → -(10-6)×0.1 = -0.4 mm 6th line → 6 × 0.1 = 0.6 mm
VSR = n × Least Count
Final Formula Result
Zero Error = 0.0 mm Correction = -0.3 mm Correction = +0.4 mm 12.0 + 0.6 = 12.6 mm
True = Observed – (±Zero Error)
💡 JEE Main Trap for Negative Zero Error in Vernier: If Vernier Zero is to the LEFT of Main Scale Zero and the 6th division coincides, the error is NOT -0.6 mm! Always subtract from total divisions: -(10 – 6) × LC = -0.4 mm.
🔩 Tap a Screw Gauge State to Inspect Circular Thimble Scale:
PITCH SCALE (1 Pitch = 1.0 mm, 100 Circular Divs) Reference Baseline 0 1mm 2mm 3mm CIRCULAR SCALE (100 Divs) LC = 1 mm / 100 = 0.01 mm 2 1 0 ← Aligns with Baseline! 99 98 6 5 4 ← 4th Div on Baseline (+0.04 mm) 3 0 (Zero is BELOW Baseline!) 0 (Zero is ABOVE Baseline!) 98 97 ← 97th Div on Baseline (-0.03 mm) 96 95 30 29 28 ← 28th Div Coincides! 27 26 ✅ Ideal Screw Gauge: Circular 0 is on Reference Line (Zero Error = 0.00 mm) ⚠️ POSITIVE ZERO ERROR: Circular 0 is BELOW baseline; 4th div coincides → Z.E. = +4 × 0.01 = +0.04 mm ❄️ NEGATIVE ZERO ERROR: Circular 0 crossed ABOVE baseline (97 coincides) → -(100 – 97)×0.01 = -0.03 mm 🎯 Wire Diameter = 3.0 mm (Last visible Pitch mark) + 28 × 0.01 mm = 3.28 mm!
Least Count (LC)
Pitch / N = 0.01 mm
1.0 mm / 100 Divs = 0.001 cm
Linear / Pitch Scale (PSR)
0.0 mm 0.0 mm (Studs Touching) 0.0 mm (Studs Touching) 3.0 mm (Visible on Sleeve)
Last uncovered mark on sleeve
Circular Scale (CSR)
0 × 0.01 = 0.00 mm 4 × 0.01 = +0.04 mm -(100-97)×0.01 = -0.03 mm 28 × 0.01 = 0.28 mm
Line matching Reference Baseline
Final Screw Gauge Output
Zero Error = 0.00 mm Subtract 0.04 mm Add 0.03 mm 3.00 + 0.28 = 3.28 mm
True = PSR + CSR – (±Zero Error)
💡 1-Second Memory Trick for Screw Gauge Zero Error:
• Zero BELOW Baseline = Positive Zero Error (+n × LC) → Subtract from observed reading.
• Zero ABOVE Baseline = Negative Zero Error (-(N – n) × LC) → Add to observed reading.

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