Zero Error in Measurements

Definition:

Zero error is the error that occurs when a measuring instrument does not read zero when it should.

• Happens due to imperfect calibration.

• Must be added or subtracted from readings to get the correct measurement.

1️⃣ Vernier Caliper

🔹 Positive Zero Error

• Zero of the vernier ahead of main scale zero.

• Measurement is larger than actual.

• Corrected Reading:

Corrected Reading=Observed Reading−Zero Error\text{Corrected Reading} = \text{Observed Reading} - \text{Zero Error}Corrected Reading=Observed Reading−Zero Error

🔹 Negative Zero Error

• Zero of vernier behind main scale zero.

• Measurement is smaller than actual.

• Corrected Reading:

Corrected Reading=Observed Reading+Zero Error\text{Corrected Reading} = \text{Observed Reading} + \text{Zero Error}Corrected Reading=Observed Reading+Zero Error

🔹 Example (Vernier)

• Observed reading = 12.6 mm

• Zero error = +0.1 mm (positive)

• Corrected length = 12.6 − 0.1 = 12.5 mm

2️⃣ Screw Gauge (Micrometer)

• Used for very small lengths (like wire diameter).

• Same concept of zero error applies.

🔹 Positive Zero Error

• Zero of thimble above main scale zero

• Corrected Reading = Observed − Zero Error

🔹 Negative Zero Error

• Zero of thimble below main scale zero

• Corrected Reading = Observed + Zero Error

🔹 Important Formulas

Corrected Reading=Observed Reading−Zero Error (if +ve)Corrected Reading=Observed Reading+Zero Error (if −ve)\text{Corrected Reading} = \text{Observed Reading} - \text{Zero Error (if +ve)} \text{Corrected Reading} = \text{Observed Reading} + \text{Zero Error (if −ve)}Corrected Reading=Observed Reading−Zero Error (if +ve)Corrected Reading=Observed Reading+Zero Error (if −ve)

🔹 How to Detect Zero Error

Vernier Caliper

• Close the jaws completely.

• Check if the zero marks coincide.

Screw Gauge

• Rotate the thimble fully closed.

• Check if the thimble zero coincides with main scale.

🔹 Key Tips for JEE Mains

1. Always check for zero error before measuring.

2. Remember the sign: + for positive error, − for negative error.

3. Apply correction after observation, not before.

4. Practice diagrams — JEE often asks you to find zero error from Vernier/Screw Gauge diagram.

🔹 Quick Summary Table