NEET Physics · Chapter 16
Simple Pendulum – Complete Notes, Revision, Important Questions & Downloads
This topic is centered on the TOC subtopic Pendulum Motion Analysis, where you model the bob as an angular SHM system under the small-angle approximation. From restoring torque tau = -mgl sin theta and sin theta approx theta for small oscillations, the equation reduces to alpha = -(g/l)theta, giving omega^2 = g/l and T = 2pi*sqrt(l/g). NEET tests this topic through direct derivation checkpoints and scenario numericals where the student must identify whether amplitude is small enough for SHM treatment before applying period formulas. A common trap is using T = 2pi*sqrt(l/g) at large amplitudes without checking the small-angle condition first.
6 SubtopicsDerivation + MCQNEET Core
Expected QuestionsQ
1
Most years include one direct or embedded question on period formula, mass-independence, or small-angle validity.
Time Required⏱
1.5-2 hours
About 45 minutes for derivation mastery and 45-60 minutes for ratio and condition-check numericals.
Difficulty⚡
Easy-Medium
Core equations are short, but wrong option selection is common when students skip effective assumptions.
NRI USA Curriculum GapUS
Medium
Many US tracks cover pendulum basics but do not repeatedly test torque-linearization and assumption-bound formula use in one-step MCQ format.
6Subtopics
8Practice Questions
4Free Downloads
2 hrsPrep Time
NEET Weightage - Simple Pendulum
Simple Harmonic Motion (Chapter 16)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 1 | 4 | |
| 2022 | 0 | 0 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| 2019 | 1 | 4 | |
| 6-Year Pattern View | 4-6 | 16-24 |
Simple pendulum questions frequently combine one conceptual condition (small angle) with one computational step (period ratio).
Mass of bob does not appear in T = 2pi*sqrt(l/g); when mass changes with fixed l and g, period remains unchanged.
Derivation-based items check the path tau = -mgl sin theta -> alpha = -(g/l)theta -> omega^2 = g/l and often place distractors around sign and l-position.
Mass of bob does not appear in T = 2pi*sqrt(l/g); when mass changes with fixed l and g, period remains unchanged.
Derivation-based items check the path tau = -mgl sin theta -> alpha = -(g/l)theta -> omega^2 = g/l and often place distractors around sign and l-position.
0.8
Avg Questions / Year
20
Total Marks (6 yrs)
Mixed
Pattern
Medium
Difficulty
How to Score in Simple Pendulum Questions
1
Write the torque equation first Start from tau = -mgl sin theta before jumping to the final period expression. This keeps the sign and geometry visible and prevents choosing options that use restoring torque in the wrong direction.
2
Check small-angle validity before formula use Apply sin theta approx theta only for small angular displacement. If the question hints at large amplitude, do not assume exact SHM period independence; this is a frequent option-level trap.
3
Use ratio form for rapid calculation For same bob and setup changes, use T2/T1 = sqrt((l2/g2)/(l1/g1)). This avoids repeated substitution and reduces arithmetic mistakes in length or gravity variation problems.
4
Treat mass as a distractor variable When options include mass scaling, revisit the derived relation omega^2 = g/l. If only mass changes, period does not change. Many NEET options are designed to trigger an incorrect sqrt(m) instinct.
Download Study Notes - Simple Pendulum
PDF · Cheat Sheet · MCQ Set · PYQFull Notes
Complete derivation from restoring torque to period expression, with condition checks for small-angle approximation and one worked angular SHM reduction example.
Download PDFFormula Sheet
One-page formula map: tau = -mgl sin theta, alpha = -(g/l)theta, omega^2 = g/l, T = 2pi*sqrt(l/g), plus the condition statement for SHM validity.
Download PDFMCQ Practice
Practice set focused on period ratios, small-angle screening, and mass-independence checkpoints with compact but complete solutions.
Download PDFPYQ
Curated previous-year style pendulum questions organized by idea type: derivation checkpoints, ratio calculation, and assumption-detection mistakes.
Download PDFSubtopics
2-Column TableRevision Cards
Concept → Trap → Example1) Pendulum Motion Analysis
Core DerivationFor small oscillations: tau = -mgl sin theta approx -mgl theta, so alpha = -(g/l)theta, therefore omega^2 = g/l and T = 2pi*sqrt(l/g).
- Always set up torque about the pivot; using force balance directly at first step often causes missing l factor errors.
- The linear SHM form appears only after the small-angle step sin theta approx theta, so this condition is part of the formula.
- Most wrong answers come from either dropping the negative sign in restoring torque or inserting bob mass into period expression.
Example (NEET-style)If l = 1.0 m and g = 9.8 m/s^2, then T = 2pi*sqrt(1.0/9.8) approx 2.01 s. If length becomes 0.25 m with the same g, period scales as sqrt(0.25) = 0.5, so new T is about 1.00 s; this confirms T depends on sqrt(l), not linearly on l.
US Curriculum Gap - Simple Pendulum
Students entering from US pathways should actively bridge two exam-style differences before solving NEET SHM sheets.AP Physics 1 vs NEET derivation strictness
AP Physics 1 usually emphasizes conceptual period dependence and graph interpretation, while NEET often expects a clean torque-to-differential-equation chain in one MCQ step.
- NEET options frequently test the intermediate relation alpha = -(g/l)theta, not only the final T formula.
- Students should practice writing the derivation in three lines without skipping sign conventions.
- Distractors are built from common derivation slips such as omega^2 = l/g or T proportional to l.
Assumption-bound formula application
Many US assignments treat the small-angle model as given, whereas NEET asks whether the model itself is applicable before calculation.
- Check if displacement is explicitly small before applying sin theta approx theta.
- If the question indicates large amplitude, recognize that exact SHM simplification is no longer valid.
- Train on mixed questions where one option is numerically neat but physically invalid due to assumption failure.
NEET-style practice questions
4 questions1A pendulum of length 1.6 m oscillates with small amplitude at a place where g = 10 m/s^2. Its time period is closest to:Pendulum Motion Analysis
2.5 s
4.0 s
1.6 s
3.2 s
Use T = 2pi*sqrt(l/g). Substituting l = 1.6 and g = 10 gives sqrt(0.16) = 0.4, so T = 2pi*0.4 = 0.8pi approx 2.51 s. Hence 2.5 s is correct. Option 4.0 s usually comes from forgetting the square root and using T proportional to l. Option 1.6 s comes from dropping the 2pi factor. Option 3.2 s comes from mixing angular frequency and period relations. This question checks direct formula application under the small-angle condition and arithmetic discipline in root evaluation.
2In deriving the SHM equation for a simple pendulum, which approximation is essential for obtaining alpha proportional to -theta?Pendulum Motion Analysis
sin theta approx theta for small theta
cos theta approx theta
tan theta approx 1/theta
g approx l
From torque tau = -mgl sin theta and rotational equation ml^2 alpha = tau, we get alpha = -(g/l)sin theta. To make this linear in displacement angle, the small-angle approximation sin theta approx theta is required. Then alpha = -(g/l)theta, which is the SHM form. Option cos theta approx theta is dimensionally and numerically wrong near zero because cos theta approx 1, not theta. Option tan theta approx 1/theta is false near small angles where tan theta approx theta. Option g approx l is physically meaningless since g and l have different dimensions.
3For a simple pendulum, the bob mass is changed from m to 4m while length and g remain unchanged. The new period is:Pendulum Motion Analysis
T/2
T
2T
sqrt(2)T
Time period for a simple pendulum in the small-angle limit is T = 2pi*sqrt(l/g), where mass does not appear. The cancellation occurs during derivation: ml^2 alpha = -mgl sin theta, so m is removed from both sides before solving for omega. Therefore changing mass from m to 4m does not alter period. Option T/2 and 2T are spring-mass intuition errors where students wrongly transfer T proportional to sqrt(m) from linear oscillator formulas. Option sqrt(2)T is another variant of the same wrong mapping. This checks whether candidates distinguish pendulum dynamics from spring-block SHM.
4A pendulum is pulled to a very large angular amplitude and released. Which statement is best for NEET-level modeling?Pendulum Motion Analysis
T = 2pi*sqrt(l/g) remains exact for all amplitudes
The small-angle SHM model is not strictly valid at large amplitude
Mass-dependence appears, so T varies as sqrt(m)
Gravity has no role at large amplitude
The formula T = 2pi*sqrt(l/g) comes from replacing sin theta with theta, which is valid only for small angular displacement. At large amplitude this approximation fails, so the motion is oscillatory but not strictly simple harmonic in the linear sense. Option A is therefore incorrect because it ignores model assumptions. Option C is false because mass cancellation is structural in the pendulum equation and does not reappear as a dominant factor this way. Option D is physically impossible since gravity supplies the restoring torque. This item tests whether students attach conditions to formulas instead of memorizing standalone expressions.
Practice Questions
Click "Reveal Answer" after attempting1If the length of a simple pendulum is increased by 44%, by what percentage does its time period increase (small oscillations)?
44%
20%
12%
22%
👁 Reveal Answer
New length l2 = 1.44l1. Since T proportional to sqrt(l), T2/T1 = sqrt(1.44) = 1.2. Therefore time period increases by 20%. Correct option is 20%. The 44% option comes from assuming linear dependence T proportional to l, which is incorrect. The 12% and 22% options arise from rough mental rounding without applying the square-root relation.
2A pendulum has period 2 s at one location. At another location its period is 2.5 s with same length. Find g2/g1.
0.64
1.56
0.80
1.25
👁 Reveal Answer
For fixed length, T proportional to 1/sqrt(g), so g proportional to 1/T^2. Therefore g2/g1 = (T1/T2)^2 = (2/2.5)^2 = (0.8)^2 = 0.64. Correct option is 0.64. Option 1.56 is inverse ratio error. Option 0.80 comes from forgetting square. Option 1.25 is direct period ratio misuse.
3A pendulum bob of mass 200 g is replaced by 50 g while keeping length and amplitude small and unchanged. Choose the correct statement.
Period becomes half
Period doubles
Period remains unchanged
Period changes by factor 2
👁 Reveal Answer
Correct statement: period remains unchanged. The period expression in small-angle model is T = 2pi*sqrt(l/g), which contains no mass term. During derivation, mass cancels from torque and inertia terms. Any option showing factor changes due to mass is incorrect transfer from spring-mass SHM intuition. This is a standard distractor design in pendulum MCQs.
4For two pendulums with lengths 0.81 m and 1.44 m at same place, find ratio of periods T1:T2.
3:4
9:16
4:3
1:2
👁 Reveal Answer
Use T proportional to sqrt(l). Hence T1:T2 = sqrt(0.81):sqrt(1.44) = 0.9:1.2 = 3:4. Correct option is 3:4. Option 9:16 results from using lengths directly. Option 4:3 is inverted ratio. Option 1:2 is over-rounding without actual square-root calculation.
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Frequently Asked Questions
Notes · Downloads · Revision · Important QuestionsWhy does bob mass cancel in simple pendulum period derivation?
The governing equations are ml^2 alpha = -mgl sin theta and, for small angles, alpha = -(g/l)theta. The common factor m appears on both sides and cancels exactly before solving for angular frequency. Once omega^2 = g/l is obtained, period becomes T = 2pi/omega = 2pi*sqrt(l/g), which contains only length and gravitational acceleration.
What is the physical reason for the negative sign in restoring torque?
The negative sign indicates direction: restoring torque acts opposite to angular displacement and tries to bring the bob back toward mean position. If theta is positive, torque is negative and vice versa. This opposite-direction relation is the defining feature of stable oscillation and is essential for writing the SHM-type equation with a negative proportionality constant.
When is T = 2pi*sqrt(l/g) not reliable as an exact period formula?
It is derived by using sin theta approx theta, so it is accurate only for small angular amplitudes. At larger amplitudes, the motion remains periodic but the linear SHM approximation is not exact and period increases slightly compared with the small-angle value. In MCQs, ignoring this condition can lead to choosing a numerically attractive but physically invalid option.
Why is pendulum length measured to the center of mass of bob?
The restoring torque depends on the lever arm from pivot to bob center of mass, not merely to the string end. Therefore effective length is the distance from suspension point to bob center of mass. If you use only thread length when bob size is non-negligible, period predictions shift systematically and ratio calculations become inconsistent with measured data.
How can I quickly compare periods at two locations with different g?
Keep length fixed and use T proportional to 1/sqrt(g). Write T2/T1 = sqrt(g1/g2) directly. This one-line ratio avoids full substitution and reduces arithmetic mistakes in exam pressure conditions. Always check the trend: if g decreases, restoring torque weakens and period must increase; if your ratio predicts the opposite, recheck inversion.
Is a pendulum question always from pure formula substitution in NEET?
Not always. Some items are direct substitutions, but many combine conceptual checks with one calculation, such as deciding whether small-angle approximation is valid, identifying mass as irrelevant, or selecting the correct proportionality before solving. Preparing only formula memory without condition and derivation awareness leaves high risk for option traps.
How do I avoid sign and proportionality errors in derivation-based MCQs?
Use a fixed three-line routine: write restoring torque with negative sign, divide by ml^2 to get angular acceleration, then apply small-angle linearization. After obtaining omega^2 = g/l, verify dimensions of omega^2 as s^-2. This structured check catches common wrong forms such as omega^2 = l/g or positive-feedback torque assumptions.
What is the fastest revision sequence for this topic before a test?
Revise in this order: core derivation, condition for approximation, ratio formulas for length and gravity changes, and mass-independence reasoning. Then solve 8-10 mixed pendulum MCQs in one sitting and classify each mistake as formula, assumption, or arithmetic. This process makes the topic retrieval-ready and reduces repeated error patterns in final practice rounds.
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