NEET 2025 Physics Vernier Calipers Numerical Question

To solve the question regarding the measurement of the diameter of a spherical object using Vernier callipers, let's break it down step-by-step.

Given Data:

1. Main Scale Reading (MSR): $M = 5 \, \text{cm}$
2. Number of coinciding Vernier Scale Divisions (VSD): $n = 8$
3. Least Count (LC) of Main Scale: $0.1 \, \text{cm}$
4. Zero Error: The zero of the Vernier scale reads at $0.1 \, \text{cm}$ when the jaws are closed.
5. Vernier Scale Divisions (VSD) to Main Scale Divisions (MSD) relationship: $10 \, \text{VSD} = 9 \, \text{MSD}$

Step 1: Calculate the Least Count of the Vernier Scale

The least count of the Vernier calipers can be calculated using the formula:

$$\text{Least Count (LC)} = \text{Value of 1 MSD} - \text{Value of 1 VSD}$$

Here, we know:

• Value of 1 MSD = $0.1 \, \text{cm}$
• Let's denote the value of 1 VSD as $x$.

From the relationship given, we have:

$$10x = 9(0.1) \implies 10x = 0.9 \implies x = 0.09 \, \text{cm}$$

Thus, the least count of the Vernier scale is:

$$\text{LC} = 0.1 \, \text{cm} - 0.09 \, \text{cm} = 0.01 \, \text{cm}$$

Step 2: Calculate the Observed Diameter

The total reading when the Vernier scale is taken into account is given by:

$$\text{Total Reading} = \text{MSR} + (n \times \text{LC})$$

Substituting the known values:

$$\text{Total Reading} = 5 \, \text{cm} + (8 \times 0.01 \, \text{cm}) = 5 \, \text{cm} + 0.08 \, \text{cm} = 5.08 \, \text{cm}$$

Step 3: Correct for Zero Error

Since the zero of the Vernier scale is at $0.1 \, \text{cm}$ when the jaws are closed, this indicates a positive zero error. To correct for this zero error, we subtract it from the total reading:

$$\text{Corrected Reading} = \text{Total Reading} - \text{Zero Error}$$

Thus:

$$\text{Corrected Reading} = 5.08 \, \text{cm} - 0.1 \, \text{cm} = 4.98 \, \text{cm}$$

Conclusion

After zero error correction, the measured diameter of the spherical object is $4.98 \, \text{cm}$.

Option Analysis

• A) 5.18 cm: Incorrect as it does not account for the zero error.
• B) 5.08 cm: This is the total reading before correcting for zero error; hence incorrect as a final answer.
• C) 4.98 cm: This is the correct answer after correcting for zero error.
• D) 5.00 cm: Incorrect as it arbitrarily presents a different value without proper justification.

Thus, the correct answer is C) 4.98 cm.