Q.160 Physics ⭐ 360° Option Elimination Active

NEET 2020 Physics Question 160 Solution

Topic: Laws of Motion · Official NTA Booklet Code E1

Question

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:

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Verified Against NTA Final Answer Key

Option (3) : g/5

📚 Laws of Motion Easy

📋 Given Parameters & Problem Setup

Mass 1 (m1) 4 kg

Mass 2 (m2) 6 kg

Pulley & String Massless, ideal and frictionless

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The 30-Second Exam Hall Shortcut: ⚡ "Atwood Machine Shortcut: a = (m2 - m1)g / (m1 + m2) = (6 - 4)g / (6 + 4) = 2g / 10 = g/5!"

⏱️ 25 seconds

For any ideal two-mass Atwood pulley system, acceleration is the ratio of net pulling force to total inertia: a = Δm · g / M_total = (6 - 4)g / (6 + 4) = 2g / 10 = g/5. Takes under 5 seconds!

1 Identify heavier mass m2 = 6 kg and lighter mass m1 = 4 kg.

2 Use standard acceleration formula:

a = \frac{m_2 - m_1}{m_1 + m_2} g

3 Substitute numbers:

a = \frac{6 - 4}{6 + 4} g = \frac{2}{10} g = \frac{g}{5}

4 Select Option (3) g/5.

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Why You Can 100% Trust This Shortcut: NCERT Physics · Laws of Motion (Connected Motion in Pulley Systems)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Identify System and Constraints

Two bodies of masses $m_1 = 4\text{ kg}$ and $m_2 = 6\text{ kg}$ are connected by a taut, inextensible, massless string passing over a frictionless fixed pulley. Both masses accelerate with equal magnitude $a$ .

Step 2

Formulate Free Body Equations (FBD)

For mass $m_2 = 6\text{ kg}$ descending downwards: $m_2 g - T = m_2 a$ For mass $m_1 = 4\text{ kg}$ ascending upwards: $T - m_1 g = m_1 a$ .

Step 3

Eliminate Tension to Find Acceleration

Add the two equations: $(m_2 g - T) + (T - m_1 g) = (m_1 + m_2) a$ $(m_2 - m_1) g = (m_1 + m_2) a$ $a = \frac{m_2 - m_1}{m_1 + m_2} g$ .

Step 4

Numerical Evaluation

Substitute $m_1 = 4\text{ kg}$ and $m_2 = 6\text{ kg}$ : $a = \frac{6 - 4}{6 + 4} g = \frac{2}{10} g = \frac{g}{5}$ . Matches Option 3.

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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; acceleration would only equal g in free fall without any resisting connected mass.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming free fall acceleration for connected systems.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; dividing net force 2g by only the lighter mass 4 kg.

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting that both masses must be accelerated by the driving force.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value; a = (6 - 4)g / (6 + 4) = 2g / 10 = g/5.

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Why this is airtight: None; rigorous application of Newton’s second law.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; assumes net pulling mass is 1 kg instead of 2 kg.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic subtraction blunder (6 - 4 = 1).

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NTA Trap Alert: Total Inertia in Atwood Systems

Dividing net driving force by one mass instead of total system inertia (m1 + m2).

🛡️ How to avoid the -1 mark: Always remember:

a = \frac{F_{\text{net, external}}}{M_{\text{total}}} = \frac{(m_2 - m_1)g}{m_1 + m_2}

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Core NEET Syllabus Standard

Physics · Laws of Motion Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Acceleration of Two-Body Connected System on a Frictionless Pulley (Atwood Machine)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 160 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "Atwood Machine Shortcut: a = (m2 - m1)g / (m1 + m2) = (6 - 4)g / (6 + 4) = 2g / 10 = g/5!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Identify System and Constraints

Formulate Free Body Equations (FBD)

Eliminate Tension to Find Acceleration

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Total Inertia in Atwood Systems

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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