Q.44 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 44 Solution

Topic: Oscillations · Official NTA Booklet Code 45

Question

Two identical point masses P and Q, suspended from two separate massless springs of spring constants k₁ and k₂, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A_Q/A_P) of the amplitude A_Q of mass Q to the amplitude A_P of mass P is:

✓

Verified Against NTA Final Answer Key

Option (4) : \sqrt{\frac{k_1}{k_2}}

📚 Oscillations Easy

📋 Given Parameters & Problem Setup

Masses Identical point masses m_P = m_Q = m

Spring Constants k₁ for spring P, k₂ for spring Q

Condition Maximum speeds are the same: v_{max, P} = v_{max, Q}

Target Ratio A_Q / A_P (amplitude of mass Q to mass P)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Conservation of Energy / v_max Shortcut

⏱️ Save ~25 seconds

v_max = A ω = A √(k/m). Equal v_max ⟹ A_P √k₁ = A_Q √k₂ ⟹ A_Q / A_P = √(k₁ / k₂)!

1 Write maximum speed in SHM: v_max = A ω.

2 Angular frequency of mass-spring system: ω = √(k / m).

3 Substitute: v_max = A √(k / m).

4 Since masses m are identical and maximum speeds are equal: A_P √(k₁) = A_Q √(k₂).

5 Solve for the requested ratio A_Q / A_P: A_Q / A_P = √(k₁ / k₂).

6 Select Option (4) in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Simple Harmonic Motion Kinematics (NCERT Physics · Oscillations: v = ω√(A² - x²)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Maximum Speed in SHM

For a particle executing simple harmonic motion with amplitude A and angular frequency ω, the maximum speed occurs at the equilibrium position:

v_{max} = A \omega = A \sqrt{\frac{k}{m}}

• Alternative derivation via energy conservation: (1/2) m v_{max}² = (1/2) k A² ⟹ v_{max} = A √(k/m).

Step 2

Equate Maximum Speeds of P and Q

Since the masses are identical and their maximum speeds are equal:

v_{max, P} = v_{max, Q} \implies A_P \sqrt{\frac{k_1}{m}} = A_Q \sqrt{\frac{k_2}{m}}

• The common mass factor √m cancels out from both sides:
• A_P \sqrt{k_1} = A_Q \sqrt{k_2}.

Step 3

Calculate the Amplitude Ratio A_Q / A_P

Rearrange the expression for the required ratio:

\frac{A_Q}{A_P} = \frac{\sqrt{k_1}}{\sqrt{k_2}} = \sqrt{\frac{k_1}{k_2}}

• Matches Option (4) perfectly.

⭐

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. Forgets square root and inverts ratio.

⚠️

Student Fallacy (Why candidates pick this trap): Equating maximum forces instead of maximum speeds and omitting square root.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Missing the square root.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming A ∝ k instead of A ∝ 1/√k.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Inverted ratio A_P / A_Q instead of A_Q / A_P.

⚠️

Student Fallacy (Why candidates pick this trap): Calculating A_P / A_Q instead of A_Q / A_P.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. A_P √k₁ = A_Q √k₂ ⟹ A_Q / A_P = √(k₁ / k₂).

💡

Why this is airtight: None; clean energy/velocity equality.

⚠️

NTA Trap Alert: Inverting Ratio (A_P / A_Q vs A_Q / A_P)

Candidates easily deduce A √k = const, but mistakenly write A_Q / A_P = √(k₂/k₁) (Option 3). Double check: A is inversely proportional to √k, so A_Q / A_P = √(k_P / k_Q) = √(k₁ / k₂)!

🛡️ How to avoid the -1 mark: Cross-multiply: A_Q · √k₂ = A_P · √k₁ ⟹ A_Q / A_P = √k₁ / √k₂.

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Oscillations Standard Benchmark

Core Scientific Principle Tested:

"v_{max} = A √(k/m); equal v_{max} implies A ∝ 1/√k."

Syllabus Focus: Velocity and Energy in Simple Harmonic Motion

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

A √k = constant ⟹ A_Q / A_P = √(k₁ / k₂)!

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NEET 2025 Physics Question 44 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Conservation of Energy / v_max Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Maximum Speed in SHM

Equate Maximum Speeds of P and Q

Calculate the Amplitude Ratio A_Q / A_P

360° Option Elimination Engine Key Feature

NTA Trap Alert: Inverting Ratio (A_P / A_Q vs A_Q / A_P)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Oscillations

Time Period of a Floating Cylindrical Cork in Liquids of Different Densities

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