Q.38 Physics · Section B ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 38 Solution

Topic: Oscillations · Official NTA Booklet Code T1

Question

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x/2 times its original time period. Then the value of x is:

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Verified Against NTA Final Answer Key

Option (4) : √2

📚 Oscillations Easy

📋 Given Parameters & Problem Setup

Mass of bob change Tripled (3m)

Length of pendulum change Halved (L / 2)

New time period expression T’ = (x / 2) T

⚡

The 30-Second Exam Hall Shortcut: ⚡ Mass Independence & Length Scaling Hack

⏱️ Save ~40 seconds

Mass of bob has ZERO effect on pendulum period (T = 2π√(L/g))! Length halved -> T’ = T / √2 = (√2 / 2) T -> x = √2!

1 Simple pendulum period: T = 2π√(L/g). Mass of the bob does NOT enter the equation!

2 Tripling mass has 0 effect.

3 Halving length: L’ = L / 2 => T’ = 2π√(L / 2g) = T / √2.

4 Match with given form: T’ = (x / 2) T => 1 / √2 = x / 2 => x = 2 / √2 = √2.

5 Option (4) in 5 seconds!

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Why You Can 100% Trust This Shortcut: Simple Pendulum Equation of Motion (Time period T = 2π√(L/g) is independent of bob mass).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Time Period of Simple Pendulum

For small angular displacements, the time period T of a simple pendulum of length L and bob mass m oscillating under gravity g is given by:

T = 2\pi \sqrt{\frac{L}{g}}

Step 2

Independence of Bob Mass

Notice that the mass m of the bob does not appear in the formula. Restoring torque and rotational inertia both scale linearly with m, so mass cancels out identically. Therefore, tripling the mass does not change the time period at all.

\frac{\partial T}{\partial m} = 0 \implies T \text{ is independent of mass}

Step 3

Effect of Halving the Length

The length is made half its original length: L’ = L / 2. The new time period T’ is:

T' = 2\pi \sqrt{\frac{L/2}{g}} = \frac{1}{\sqrt{2}} \left(2\pi \sqrt{\frac{L}{g}}\right) = \frac{T}{\sqrt{2}}

Step 4

Solving for Parameter x

We are given that T’ = (x / 2) T. Equating the two expressions:

\frac{x}{2} T = \frac{1}{\sqrt{2}} T \implies \frac{x}{2} = \frac{1}{\sqrt{2}} \implies x = \frac{2}{\sqrt{2}} = \sqrt{2}

⭐

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:

Includes the factor of 3 from mass tripling.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming period is proportional to √mass.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect algebra.

⚠️

Student Fallacy (Why candidates pick this trap): Squaring instead of square rooting.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Uses the mass factor 3 instead of the length factor.

⚠️

Student Fallacy (Why candidates pick this trap): Thinking T depends on mass.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact result: 1/√2 = x/2 -> x = √2.

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Why this is airtight: None.

⚠️

NTA Trap Alert: Including the Bob Mass in Pendulum Period

NTA includes √3 and 2√3 to bait students who mistakenly recall spring-mass formula T = 2π√(m/k) instead of pendulum formula T = 2π√(L/g).

🛡️ How to avoid the -1 mark: Pendulum period depends ONLY on Length and Gravity, NEVER on Mass!

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Core NEET Syllabus Standard

Physics Core Oscillations · Oscillations Standard Benchmark

Core Scientific Principle Tested:

"The period of a simple pendulum is T = 2π√(L/g), independent of mass and amplitude (for small angles)."

Syllabus Focus: The Simple Pendulum

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Mass doesn’t matter for a pendulum string: Length cut in half makes x equal √2 king!

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NEET 2024 Physics Question 38 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Mass Independence & Length Scaling Hack

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Time Period of Simple Pendulum

Independence of Bob Mass

Effect of Halving the Length

Solving for Parameter x

360° Option Elimination Engine Key Feature

NTA Trap Alert: Including the Bob Mass in Pendulum Period

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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