JEE PYQ: Units & Measurements - Question ID 32f827e3012f (JEE Main 2026)

Core Formula & Concept:

In a Vernier calipers, the least count (LC) is the smallest length that can be measured accurately. It is given by:

$\text{Least Count (LC)} = \frac{\text{Value of 1 main scale division}}{\text{Total number of Vernier scale divisions}}$

When the jaws of the Vernier calipers are closed (touching each other), the zero of the Vernier scale may not align with the zero of the main scale. This misalignment is called the zero error. If the zero of the Vernier scale lies to the right of the main scale zero, the zero error is positive. Conversely, if it lies to the left, the zero error is negative.

The magnitude of the zero error is calculated as:

$\text{Zero Error} = n \times \text{Least Count}$

where $n$ is the number of Vernier divisions that coincide with a main scale division when the jaws are closed.

Step-by-Step Derivation:

Step 1: Determine the Least Count (LC)
Given:

• Value of 1 main scale division = $1 \text{ mm}$
• Total Vernier scale divisions = $10$

Using the formula for least count: $\text{LC} = \frac{1 \text{ mm}}{10} = 0.1 \text{ mm}$ Step 2: Analyze the Zero Error Condition
The question states:

• The zero of the Vernier scale is shifted to the right of the main scale zero.
• The $7^{\text{th}}$ Vernier division coincides with a main scale reading.

Since the zero of the Vernier scale is to the right of the main scale zero, the zero error is positive. Step 3: Calculate the Zero Error
The zero error is given by: $\text{Zero Error} = n \times \text{LC}$ Here, $n = 7$ (since the $7^{\text{th}}$ division coincides), and $\text{LC} = 0.1 \text{ mm}$. Thus: $\text{Zero Error} = 7 \times 0.1 \text{ mm} = 0.7 \text{ mm}$ Step 4: Convert to Centimeters
Since $1 \text{ cm} = 10 \text{ mm}$, we convert $0.7 \text{ mm}$ to centimeters: $0.7 \text{ mm} = \frac{0.7}{10} \text{ cm} = 0.07 \text{ cm}$ Step 5: Combine Results
The zero error is positive and has a magnitude of $0.07 \text{ cm}$. Therefore, the correct description is: 0.07 cm positive zero error. Conclusion: The correct option is C. Common Traps & Exam Tip:

1. Misidentifying the Sign of Zero Error:
Students often confuse the direction of the zero error. Remember:

• If the Vernier zero is to the right of the main scale zero, the zero error is positive.
• If the Vernier zero is to the left, the zero error is negative.

In this question, the zero is shifted to the right, so the error is positive. 2. Incorrect Least Count Calculation:
Some students mistakenly take the least count as $1 \text{ mm}$ instead of $0.1 \text{ mm}$. Always divide the main scale division by the number of Vernier divisions. 3. Unit Conversion Errors:
The options are given in centimeters, but the least count is in millimeters. Failing to convert $0.7 \text{ mm}$ to $0.07 \text{ cm}$ leads to selecting option D instead of C. 4. Coinciding Division Misinterpretation:
The question states that the $7^{\text{th}}$ Vernier division coincides with a main scale reading. Some students assume this means the zero error is $7 \text{ mm}$, ignoring the least count. Always multiply the coinciding division number by the least count. Exam Tip:
When solving Vernier calipers problems:

1. First, calculate the least count.
2. Determine the direction of the zero error (positive or negative).
3. Multiply the coinciding division number by the least count to find the magnitude.
4. Convert units if necessary (e.g., mm to cm).
5. Match your result with the given options.