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Physics Question 28 – NEET-UG 2024

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In a vernier calipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is :

The vernier constant (or least count) is the difference between one main scale division (MSD) and one vernier scale division (VSD).

Step 1: Establish the relationship between MSD and VSD✦ Active

According to the problem statement, (N+1) divisions of the vernier scale coincide with N divisions of the main scale. This can be written as:

(N+1) VSD=N MSD

From this, we can express one vernier scale division (VSD) in terms of one main scale division (MSD):

1 VSD=NN+1 MSD
💡 Teacher's Secret Hint

Remember that the vernier constant is always positive, representing the smallest measurement that can be made.

Step 2: Calculate the Vernier Constant (VC)○ Expand

The vernier constant (VC) is defined as the difference between one main scale division and one vernier scale division:

VC=1 MSD−1 VSD

Substitute the expression for 1 VSD from Step 1:

VC=1 MSD−NN+1 MSD

Factor out 1 MSD:

VC=MSD(1−NN+1)=MSD(N+1−NN+1)=MSD(1N+1)
💡 Teacher's Secret Hint

This formula for VC is standard when (N+1) VSD coincides with N MSD.

Step 3: Substitute given values and convert units○ Expand

We are given that 1 MSD = 0.1 mm. Substitute this into the VC formula:

VC=(0.1 mm)×1N+1

The question asks for the vernier constant in centimeters. We know that 1 cm = 10 mm, so 1 mm = 0.1 cm. Therefore, 0.1 mm = 0.1×0.1 cm = 0.01 cm.

VC=(0.01 cm)×1N+1=1100×1N+1 cm

Thus, the vernier constant is:

VC=1100(N+1) cm

Comparing this with the given options, option (1) matches our result.

💡 Teacher's Secret Hint

Always pay attention to the required units in the final answer. A common mistake is forgetting unit conversion.

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