Q.10 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 10 Solution

Topic: Oscillations · Official NTA Booklet Code M1

Question

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is:

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Verified Against NTA Final Answer Key

Option (4) : 0.628 s

📚 Oscillations Easy

📋 Given Parameters & Problem Setup

Stretching Force (F) 10 N

Extension (x) 5 cm = 0.05 m

Suspended Mass (m) 2 kg

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The 30-Second Exam Hall Shortcut: ⚡ 2-Step SHM: k = F/x = 200 N/m, T = 2π√(m/k)

⏱️ Save ~20 seconds

$k = \frac{10}{0.05} = 200\text{ N/m}$ . Time period $T = 2\pi \sqrt{\frac{2}{200}} = 2\pi \sqrt{\frac{1}{100}} = \frac{2\pi}{10} = \frac{6.283}{10} = 0.628\text{ s}$ ! Instant 15-second calculation matching Option (4)!

1 Compute spring constant:

k = \frac{F}{x} = \frac{10\text{ N}}{0.05\text{ m}} = 200\text{ N/m}

2 Formula for time period of mass-spring oscillator:

T = 2\pi \sqrt{\frac{m}{k}}

3 Substitute values:

T = 2\pi \sqrt{\frac{2}{200}} = 2\pi \times \frac{1}{10} = \frac{2 \times 3.1416}{10}

T = 0.628\text{ s}

5 Match Option (4).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Hooke's law and simple harmonic motion time period relation.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Determining the Spring Constant (k)

By Hooke's law, the restoring force is proportional to elongation: $F = kx$ . Given $F = 10\text{ N}$ for extension $x = 5\text{ cm} = 5 \times 10^{-2}\text{ m}$ :

k = \frac{F}{x} = \frac{10\text{ N}}{5 \times 10^{-2}\text{ m}} = 200\text{ N/m}

Step 2

Applying the Simple Harmonic Motion Time Period Equation

For a block of mass $m = 2\text{ kg}$ oscillating on an ideal spring of stiffness $k$ :

T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{2\text{ kg}}{200\text{ N/m}}} = 2\pi \sqrt{\frac{1}{100}} = \frac{2\pi}{10}\text{ s}

Step 3

Numerical Evaluation

Substitute $\pi \approx 3.1416$ :

T = \frac{2 \times 3.1416}{10} = \frac{6.2832}{10} = 0.6283\text{ s} \approx 0.628\text{ s}

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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 1

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10 due to an erroneous $x = 0.5\text{ m}$ conversion error.

⚠️

Student Fallacy (Why candidates pick this trap): Decimal place arithmetic error.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Forgets to divide by 10 from $\sqrt{1/100} = 1/10$ .

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting the denominator in

2\pi / 10

3 3

✗ Incorrect

Verdict & Scientific Reason:

Calculates $\pi$ instead of $2\pi / 10$ .

⚠️

Student Fallacy (Why candidates pick this trap): Using

T = \pi \sqrt{m/k}

without the factor of 2.

4 4

✓ 100% Correct

Verdict & Scientific Reason:

Exact time period of the spring-mass oscillator.

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Why this is airtight: None; flawless Hooke's law and SHM calculation.

⚠️

NTA Trap Alert: Centimeter to Meter Conversion Trap

Taking $x = 5$ instead of $0.05\text{ m}$ leads to $k = 2\text{ N/m}$ and $T = 6.28\text{ s}$ (Option 2). Converting $\text{cm}$ to $\text{m}$ is critical.

🛡️ How to avoid the -1 mark: Always convert distances into SI base units:

5\text{ cm} = 0.05\text{ m}

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Core NEET Syllabus Standard

NCERT Physics · Oscillations Standard Benchmark

Core Scientific Principle Tested:

"The time period of a mass $m$ attached to a spring of force constant $k$ is $T = 2\pi \sqrt{m/k}$ ."

Syllabus Focus: Simple Harmonic Motion (Spring-Mass System)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 10 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ 2-Step SHM: k = F/x = 200 N/m, T = 2π√(m/k)

Step-by-Step Rigorous Workflow & Mathematical Proof

Determining the Spring Constant (k)

Applying the Simple Harmonic Motion Time Period Equation

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Centimeter to Meter Conversion Trap

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

Condition for a Circular Phase Space Trajectory in Simple Harmonic Motion

Spring-Mass System with Slowly Leaking Mass (Variable Mass SHM)

Ratio of Amplitudes for Identical Masses with Equal Maximum Speeds

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