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Q.146 Physics ⭐ 360° Option Elimination Active
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NEET 2020 Physics Question 146 Solution

Topic: Units and Measurements · Official NTA Booklet Code E1
NEET 2020 Physics Question 146: Screw Gauge Formula: Pitch = Least Count × Number of Circular Scale Divisions

Question

A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is:

✓
Verified Against NTA Final Answer Key
Option (3) : 0.5 mm
📚 Units and Measurements Easy
📋 Given Parameters & Problem Setup
Instrument Screw gauge
Least Count (LC) 0.01 mm
Number of Circular Scale Divisions (CSD) 50
Formula Least Count = Pitch / CSD
Question Objective Calculate the pitch of the screw gauge
⚡

The 30-Second Exam Hall Shortcut: ⚡ "Pitch = Least Count × Circular Scale Divisions = 0.01 mm × 50 = 0.5 mm!"

⏱️ 15 seconds

The fundamental formula of a screw gauge is Least Count=PitchTotal circular scale divisions\text{Least Count} = \frac{\text{Pitch}}{\text{Total circular scale divisions}}. Rearranging gives Pitch=Least Count×Divisions=0.01 mm×50=0.5 mm\text{Pitch} = \text{Least Count} \times \text{Divisions} = 0.01\text{ mm} \times 50 = 0.5\text{ mm}. Mark Option (3) in 5 seconds!

1 Formula: Least Count (LC) = Pitch / Number of Circular Divisions (N).
2 Rearrange: Pitch = LC × N.
3 Substitute values: LC = 0.01 mm, N = 50.
4 Calculate: Pitch = 0.01 mm × 50 = 0.5 mm.
5 Select Option (3) 0.5 mm.
🛡️
Why You Can 100% Trust This Shortcut: NCERT Physics · Units and Measurements (Measurement of Length: Screw Gauge Principles)
📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Define Pitch and Least Count of a Screw Gauge

The pitch of a screw gauge is the linear distance advanced by the screw on the main scale when the circular cap/thimble is rotated through one complete revolution (360∘360^\circ). The least count (LC\text{LC}) is the smallest distance that can be measured using the instrument, given by: LC=PitchTotal number of divisions on circular scale (N)\text{LC} = \frac{\text{Pitch}}{\text{Total number of divisions on circular scale } (N)}

Step 2

Rearrange for Pitch

Pitch=LC×N\text{Pitch} = \text{LC} \times N

Step 3

Substitute Given Numerical Values

Given: - Least count = 0.01 mm0.01\text{ mm} - Total circular scale divisions N=50N = 50 Pitch=0.01 mm×50=0.50 mm=0.5 mm\text{Pitch} = 0.01\text{ mm} \times 50 = 0.50\text{ mm} = 0.5\text{ mm}

Step 4

Confirm Match with Options

The pitch is precisely 0.5 mm0.5\text{ mm}, which corresponds directly to Option (3).

⭐

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 A
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; 0.01 mm is the least count itself, not the pitch.

⚠️
Student Fallacy (Why candidates pick this trap): Confusing least count with pitch.
2 B
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; arithmetic error.

⚠️
Student Fallacy (Why candidates pick this trap): Multiplying by 25 instead of 50.
3 C
✓ 100% Correct
Verdict & Scientific Reason:

Factually and mathematically exact; Pitch=0.01 mm×50=0.5 mm\text{Pitch} = 0.01\text{ mm} \times 50 = 0.5\text{ mm}.

💡
Why this is airtight: None; textbook measurement calculation.
4 D
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; 1.0 mm would be the pitch if there were 100 circular divisions (0.01×1000.01 \times 100), but this screw gauge has 50 divisions.

⚠️
Student Fallacy (Why candidates pick this trap): Assuming a standard 100-division screw gauge.
⚠️

NTA Trap Alert: 50 Divisions vs 100 Divisions

Many lab screw gauges have 100 divisions (Pitch = 1 mm). But read this problem: It explicitly specifies 50 divisions! Pitch = 0.01×50=0.5 mm0.01 \times 50 = 0.5\text{ mm}.

🛡️ How to avoid the -1 mark: Always check the number of divisions given: 50 divisions -> Pitch = 0.5 mm!
📖

Core NEET Syllabus Standard

Physics · Units and Measurements Standard Benchmark
Core Scientific Principle Tested:

""

Syllabus Focus: Screw Gauge Formula: Pitch = Least Count × Number of Circular Scale Divisions
✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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