🔧 What is a Vernier Callipers?
A vernier calipers is a precise measuring instrument used to measure:
Length
Diameter (internal & external)
Depth
It is more accurate than a normal ruler.
⚙️ How Vernier Callipers Measures
It has two scales:
1. Main Scale
Fixed scale (like a ruler)
Gives measurement in cm or mm
2. Vernier Scale
Sliding scale
-
Helps measure very small differences more accurately
🧠 Working Principle
The idea is simple:
👉 The vernier scale divisions are slightly smaller than the main scale divisions
Because of this:
-
At any position, one line on the vernier scale exactly matches one line on the main scale
That matching line tells you the extra fraction to add
📏 How to Take Reading
-
Note Main Scale Reading (MSR)
→ The value just before the zero of vernier scale -
Find Vernier Coincidence (VSR)
→ Which vernier line exactly matches a main scale line -
Final Reading Formula
$ \text{Measurement} = \text{MSR} + (\text{VSR} \times \text{Least Count}) $
📉 What is Least Count?
👉 Least Count = Smallest measurement the instrument can measure
For vernier calipers:
$\text{Least Count} = \text{Value of 1 Main Scale Division} - \text{Value of 1 Vernier Scale Division}$
📊 Common Example
-
1 Main Scale Division (MSD) = 1 mm
-
10 Vernier divisions = 9 mm
So,
-
1 Vernier Division = 9/10 = 0.9 mm
$\text{Least Count} = 1 - 0.9 = 0.1 \text{ mm}$
🎯 Final Understanding
-
Main scale gives whole part
-
Vernier scale gives fractional part
-
Least count tells precision
💡 Easy Analogy
Think of it like:
-
Main scale = whole number
-
Vernier scale = decimal part
JEE Main–level PYQ-style questions on Vernier Callipers (Units & Measurements).
🔬 Vernier Callipers –
Practice Questions (JEE Main Level)
Q1. Least Count Concept
A Vernier calipers has 10 divisions on the Vernier scale coinciding with 9 divisions on the main scale. If one main scale division = 1 mm, the least count is:
A. 0.1 mm
B. 0.01 mm
C. 0.2 mm
D. 0.05 mm
Q2. Reading with Zero Error
The main scale reading is 2.3 cm and the 6th Vernier division coincides. Least
count = 0.01 cm. Zero error = +0.02 cm.
Find the corrected reading.
Q3. Negative Zero Error
A Vernier calipers shows a zero error of −0.03 cm. The observed reading of a
rod is 5.24 cm.
Find the actual length.
Q4. Backlash-Type Concept
While measuring, the Vernier reading fluctuates between 8th and 9th division.
Least count = 0.01 cm.
Estimate the uncertainty in measurement.
Q5. Diameter Measurement
The diameter of a sphere is measured as:
Main scale reading = 1.2 cm
Vernier coincidence = 5
Least count =
0.01 cm
Find the volume of the sphere (approx).
Q6. Conversion Trick
A Vernier calipers has least count 0.02 mm. Express it in cm.
Q7. Advanced Coincidence Logic
In a Vernier calipers, 50 Vernier divisions coincide with 49 main scale
divisions.
If 1 MSD = 1 mm, find least count.
Q8. Internal vs External Measurement
Which part of Vernier calipers is used to measure:
Internal diameter
Depth
A. Lower jaws, depth rod
B. Upper jaws, depth rod
C. Lower jaws,
upper jaws
D. Depth rod, lower jaws
Q9. Error Propagation
If the least count is 0.01 cm, what is the percentage error in measuring a length of 2 cm?
Q10. Trick Question (JEE Style)
A Vernier calipers gives the following readings:
MSR = 3.4 cm
Vernier coincidence = 7
Least count = 0.01 cm
Zero error = −0.02 cm
Final reading is:
A. 3.45 cm
B. 3.47 cm
C. 3.49 cm
D. 3.43 cm