Q.14 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 14 Solution

Topic: Units and Measurements · Official NTA Booklet Code T1

Question

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:

✓

Verified Against NTA Final Answer Key

Option (4) : 1 / [100(N + 1)]

📚 Units and Measurements Easy

📋 Given Parameters & Problem Setup

Vernier scale divisions (VSD) relation (N + 1) VSD = N MSD

Value of 1 Main Scale Division (MSD) 1 MSD = 0.1 mm

Target units Vernier constant in cm

⚡

The 30-Second Exam Hall Shortcut: ⚡ Least Count Formula Shortcut

⏱️ Save ~45 seconds

LC = 1 MSD - 1 VSD = 1 MSD / (N + 1); 0.1 mm = 0.01 cm = 1/100 cm -> LC = 1 / [100(N + 1)] cm!

1 Least count LC = 1 MSD - 1 VSD = 1 MSD × [1 - N/(N + 1)] = 1 MSD / (N + 1).

2 Convert 1 MSD from mm to cm: 1 MSD = 0.1 mm = 0.01 cm = 1/100 cm.

3 Substitute: LC = (1/100) / (N + 1) = 1 / [100(N + 1)] cm.

4 Option (4) is identified in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Principle of Vernier Scale (Vernier Constant = 1 MSD - 1 VSD).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition of Vernier Constant

The Vernier Constant (also known as the Least Count) of a Vernier caliper is the difference between the length of one main scale division (MSD) and one vernier scale division (VSD):

\text{VC} = 1\,\text{MSD} - 1\,\text{VSD}

Step 2

Relation Between VSD and MSD

We are given that (N + 1) divisions of the vernier scale coincide with N divisions of the main scale:

(N + 1)\,\text{VSD} = N\,\text{MSD} \implies 1\,\text{VSD} = \left(\frac{N}{N + 1}\right)\,\text{MSD}

Step 3

Substitution into Vernier Constant Formula

Substituting 1 VSD into the definition of VC:

\text{VC} = 1\,\text{MSD} - \left(\frac{N}{N + 1}\right)\,\text{MSD} = \left(1 - \frac{N}{N + 1}\right)\,\text{MSD} = \left(\frac{1}{N + 1}\right)\,\text{MSD}

Step 4

Unit Conversion to Centimeters

We are given 1 MSD = 0.1 mm. Expressing this in centimeters:

1\,\text{MSD} = 0.1\,\text{mm} = \frac{0.1}{10}\,\text{cm} = 0.01\,\text{cm} = \frac{1}{100}\,\text{cm}

Step 5

Final Expression

Substituting 1 MSD = 1/100 cm into the VC equation:

\text{VC} = \frac{1}{100(N + 1)}\,\text{cm}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Dimensionally invalid for least count.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying instead of dividing.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Dimensionally invalid.

⚠️

Student Fallacy (Why candidates pick this trap): Inverting the division.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect denominator factor and missing (N + 1).

⚠️

Student Fallacy (Why candidates pick this trap): Using N instead of (N + 1) and forgetting millimeter to centimeter conversion.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact derivation: 1 MSD / (N + 1) with 1 MSD = 1/100 cm.

💡

Why this is airtight: None.

⚠️

NTA Trap Alert: Target Unit Oversight (mm vs cm)

The question explicitly asks for the vernier constant in cm, whereas 1 MSD is given in mm. Forgetting to divide by 10 leads to 1 / [10(N + 1)].

🛡️ How to avoid the -1 mark: Always circle the requested unit in the prompt: "(in cm)".

📖

Core NEET Syllabus Standard

Physics Core Experimental Skills · Units and Measurements Standard Benchmark

Core Scientific Principle Tested:

"Least Count = 1 MSD - 1 VSD = (1 MSD) / (Number of vernier divisions)."

Syllabus Focus: Measurement of Length and Vernier Calipers

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

1 MSD over total VSDs: 0.1 mm is 1/100 cm, so 100 goes in the bottom!

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NEET 2024 Physics Question 14 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Least Count Formula Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition of Vernier Constant

Relation Between VSD and MSD

Substitution into Vernier Constant Formula

Unit Conversion to Centimeters

Final Expression

360° Option Elimination Engine Key Feature

NTA Trap Alert: Target Unit Oversight (mm vs cm)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Units and Measurements

Vernier Calliper Negative Zero Error & Full Marks Bonus Audit

Dimensional Analysis of Combined Thermal Radiation Constants (sigma_s * k_B^-1 * b)

Vernier Callipers Least Count, Positive Zero Error & Corrected Reading

Percentage Error in Physical Quantity P = a³ b² / (c √d)

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