Question

When both jaws of a vernier calipers touch each other, zero mark of the vernier scale is right to the zero mark of main scale. 4th mark on vernier scale coincides with a certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5th division of vernier scale coincides with a main scale division. Measured length of cylinder is ________ mm. (Least count of Vernier calliper = \(0.1\) mm)

• A. \(15.4\)
• B. \(15.5\)
• C. \(15.9\)
• D. \(15.1\)

Hint:

Positive zero error is subtracted, while negative zero error is added to the observed reading.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Accurate measurement with vernier callipers requires accounting for zero error. If the vernier zero is to the right of the main scale zero, it is a positive zero error.
Step 2: Key Formula or Approach:
Zero Error (\(e\)) = \(+(\text{Coinciding VSD} \times \text{LC})\)
Observed Reading = MSR + \((\text{VSR} \times \text{LC})\)
Corrected Reading = Observed Reading \(-\) Zero Error
Step 3: Detailed Explanation:
1. Calculation of Zero Error:
Vernier zero is to the right \(\Rightarrow\) Positive Zero Error.
Coinciding division = 4.
Zero Error (\(e\)) = \(+(4 \times 0.1) = +0.4 \text{ mm}\).
2. Calculation of Observed Reading:
Main Scale Reading (MSR) = 15 divisions (assuming 1 div = 1 mm) = \(15 \text{ mm}\).
Vernier Scale Reading (VSR) = 5.
Observed Reading = \(15 + (5 \times 0.1) = 15.5 \text{ mm}\).
3. Calculation of Corrected Reading:
True Length = Observed Reading \(-\) Zero Error
True Length = \(15.5 - (+0.4) = 15.1 \text{ mm}\).
Step 4: Final Answer:
The measured length of the cylinder is \(15.1 \text{ mm}\).