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CBSE Class 11 Physics Chapter 6 System of Particles and Rotational Motion Worksheet with Answers

System of Particles and Rotational Motion forms a foundation of mechanics in CBSE Class 11 Physics, introducing students to concepts such as centre of mass, torque, angular momentum, moment of inertia and rolling motion. The 2025 board exam pattern expects numerical proficiency, conceptual clarity and application skills across MCQs, short answers and long HOTS questions. This printable worksheet mirrors the actual board exam structure, providing targeted practice for NCERT Class 11 Physics Chapter 6.

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Key takeaways

  • ✓Worksheet covers all key topics: centre of mass, torque, angular momentum, moment of inertia and rolling motion per NCERT Class 11 Physics Chapter 6.
  • ✓Includes 6 MCQs, 5 fill-in-the-blanks, 10 match/true-false items, 5 short-answer questions and 3 HOTS questions for complete practice.
  • ✓One case-study question integrates real-world scenarios to develop application and analytical skills required in CBSE board exams.
  • ✓Full answer key with step-by-step explanations enables independent learning and instant feedback for self-assessment.
  • ✓Designed for 90-minute practice session; difficulty level moderate to challenging, ideal for term-end revision and pre-board drills.
  • ✓CBSETUTOR.ai offers 24×7 AI-powered doubt solving including photo-upload step-by-step solutions at a flat ₹999/month with a 3-day free trial.
  • ✓Printable PDF format allows offline practice — perfect for timed tests, homework assignments and weekend revision for Class 11 CBSE students.

Quick Chapter Recap – System of Particles and Rotational Motion

Before you begin the worksheet, recall the core definitions and formulae from NCERT Class 11 Physics Chapter 6. The centre of mass of a system is the point where the entire mass can be assumed to be concentrated for translational motion; for two particles, it lies on the line joining them and divides it in the inverse ratio of masses. Torque (τ) is the rotational analogue of force: τ = r × F, where r is the position vector from the axis to the point of application. Angular momentum (L) is L = r × p or L = Iω for rigid bodies, where I is the moment of inertia. The moment of inertia depends on mass distribution and the axis chosen; for a ring about its central axis I = MR², for a disc I = ½MR², and for a solid sphere I = ⅖MR². Rolling motion combines translation and rotation: v_cm = ωR for pure rolling without slipping. Parallel-axis theorem states I = I_cm + Md², and perpendicular-axis theorem holds for planar objects. These principles underpin all questions in this worksheet and are critical for CBSE Class 11 board preparation.
  • Centre of mass formula for discrete particles: X_cm = (Σm_i x_i) / (Σm_i); for continuous bodies, integrate ∫x dm / ∫dm.
  • Torque τ = r F sin θ; direction given by right-hand rule; net torque causes angular acceleration α = τ/I.
  • Angular momentum L = Iω; conserved when external torque is zero; relates to linear momentum as L = r × p.
  • Moment of inertia I depends on axis; use parallel-axis and perpendicular-axis theorems to calculate for shifted axes.
  • Rolling motion: KE_total = ½Mv²_cm + ½Iω²; for pure rolling KE = ½Mv²(1 + k²), where k = radius of gyration.

Worksheet Instructions and Suggested Time

This worksheet is designed for a 90-minute focused practice session. Work through each section sequentially: Section A (MCQs) should take approximately 12 minutes, Section B (fill-in-the-blanks) about 10 minutes, Section C (match or true/false) roughly 8 minutes, Section D (short-answer questions) around 30 minutes, Section E (long-answer HOTS) about 25 minutes, and the case-study question 15 minutes. Keep a calculator, NCERT textbook and formula sheet handy. Attempt all questions on your own first, then cross-check against the answer key provided at the end. Mark questions you found difficult and revisit those topics in your Class 11 Physics notes. This iterative approach builds exam confidence and highlights knowledge gaps early. The difficulty level is moderate to challenging, calibrated to mirror the rigour of CBSE board paper and competitive screening tests like JEE Mains. Print this worksheet or work on a tablet; time yourself strictly to simulate exam conditions.
  • Total time: 90 minutes; section-wise breakup ensures balanced pacing across question types.
  • Difficulty: moderate to challenging; suitable for term-2 revision and pre-board practice.
  • Materials needed: calculator, rough notebook, NCERT Class 11 Physics textbook, formula sheet.
  • Self-assessment: attempt independently, then use the detailed answer key to score and learn.
  • Iterative practice: re-do flagged questions after reviewing NCERT explanations or CBSETUTOR.ai doubt-solving videos.

Section A – Multiple Choice Questions (1 mark each)

This section contains six multiple-choice questions testing fundamental concepts, formulae recall and quick application skills from System of Particles and Rotational Motion. Each question carries one mark. Choose the most appropriate option and write the letter (A/B/C/D) in your answer sheet. No negative marking, but attempt all for maximum practice. These MCQs are representative of the objective questions appearing in CBSE Class 11 term exams and JEE Mains physics papers. Topics span centre of mass, torque, angular momentum, moment of inertia and rolling dynamics. Read each stem carefully; sometimes two options appear similar but differ in sign, direction or units. Time limit for Section A: 12 minutes.
  • Q1. The centre of mass of a two-particle system divides the line joining them in the ratio (A) m₁:m₂ (B) m₂:m₁ (C) m₁²:m₂² (D) √m₁:√m₂
  • Q2. A thin uniform rod of length L and mass M rotates about an axis perpendicular to its length passing through one end. Its moment of inertia is (A) ML²/12 (B) ML²/3 (C) ML²/2 (D) ML²/6
  • Q3. If the angular momentum of a body increases by 50%, its kinetic energy of rotation increases by (A) 50% (B) 100% (C) 125% (D) 150%
  • Q4. A solid sphere and a hollow sphere of equal mass and radius roll down an incline without slipping. Which reaches the bottom first? (A) Solid sphere (B) Hollow sphere (C) Both simultaneously (D) Depends on angle of incline
  • Q5. Torque is maximum when the angle between the position vector and force is (A) 0° (B) 45° (C) 90° (D) 180°
  • Q6. A disc and a ring of same mass and radius roll on a plane surface. The ratio of their kinetic energies (disc:ring) is (A) 3:4 (B) 4:3 (C) 1:1 (D) 2:3

Section B – Fill in the Blanks (1 mark each)

Complete each sentence with the correct term, formula, unit or numerical value. Write your answer in the blank space provided. These five questions test vocabulary, formula fluency and unit awareness from NCERT Class 11 Physics Chapter 6. Pay attention to significant figures and standard SI units. Keywords such as 'centre of mass', 'torque', 'angular momentum', 'moment of inertia', 'rolling motion', 'radius of gyration' and 'parallel-axis theorem' are all fair game. Time allocation: 10 minutes for Section B.
  • Q7. The SI unit of torque is __________.
  • Q8. For a system of particles, if the net external force is zero, the __________ moves with uniform velocity or remains at rest.
  • Q9. The moment of inertia of a thin circular ring of mass M and radius R about its diameter is __________.
  • Q10. The perpendicular-axis theorem is applicable only to __________ (planar/three-dimensional) bodies.
  • Q11. In pure rolling motion without slipping, the relationship between linear velocity v of the centre of mass and angular velocity ω is v = ω × __________.

Section C – Match the Following / True or False (1 mark each, 10 items total)

Part I contains a matching exercise with five items in Column A and five corresponding entries in Column B. Write the correct pairs (e.g. 1–D, 2–A, etc.). Part II contains five statements; mark each as True (T) or False (F). This section reinforces conceptual associations and common misconceptions in System of Particles and Rotational Motion. Total marks: 10 (1 mark per item). Suggested time: 8 minutes. Be precise; partial matches or vague reasoning will not earn credit. Refer to NCERT definitions and theorems when in doubt.
  • Part I – Match the Following:
  • Column A: (1) Centre of mass (2) Torque (3) Angular momentum (4) Radius of gyration (5) Rolling motion
  • Column B: (A) r × F (B) Conserved when external torque is zero (C) Weighted mean position of mass distribution (D) Distance from axis where entire mass can be assumed concentrated (E) Combines translation and rotation
  • Part II – True or False:
  • Q16. The centre of mass of a rigid body always lies within the material of the body. (T/F)
  • Q17. Torque is a vector quantity and its direction is given by the right-hand rule. (T/F)
  • Q18. Moment of inertia is independent of the choice of axis. (T/F)
  • Q19. A solid cylinder has a smaller moment of inertia than a hollow cylinder of the same mass and radius about the central axis. (T/F)
  • Q20. Angular momentum is always conserved in the absence of external forces. (T/F)

Section D – Short Answer Questions (2–3 marks each)

Answer the following five questions in 30–50 words or 2–3 calculation steps each. Marks are allocated for correct formula application, logical steps and final answer with units. These short-answer questions are typical of CBSE board paper Section B and require conceptual clarity plus numerical accuracy. Show all working; marks may be awarded for method even if the final answer is incorrect. Time allocation: 30 minutes for Section D. Use standard symbols and write neatly to facilitate self-checking against the answer key.
  • Q21. (2 marks) Define the centre of mass of a system of particles. State the formula for the position of the centre of mass for a two-particle system.
  • Q22. (2 marks) A force of 10 N acts at a point (2,0,0) m in the x-direction. Calculate the torque about the origin.
  • Q23. (3 marks) State the theorem of perpendicular axes. Use it to find the moment of inertia of a uniform disc of mass M and radius R about a diameter.
  • Q24. (2 marks) A solid sphere of radius R rolls without slipping on a horizontal surface with linear speed v. Derive the expression for its total kinetic energy.
  • Q25. (3 marks) Explain the physical significance of the radius of gyration. How is it related to the moment of inertia?

Section E – Long Answer and HOTS Questions (4–5 marks each)

Attempt these three higher-order thinking questions in 80–120 words or detailed calculation steps. Each carries 4–5 marks and tests derivation skills, multi-step problem solving and conceptual integration across topics in System of Particles and Rotational Motion. Marks are distributed across formula statement, substitution, algebraic manipulation, final answer and unit consistency. CBSE board long-answer questions often ask for derivations from first principles or application to compound systems. Allocate 25 minutes for Section E. Show intermediate steps clearly and box your final answers. These HOTS questions are designed to challenge students aiming for 90+ percentage and are excellent preparation for competitive exams like JEE Mains and NEET physics.
  • Q26. (5 marks) Derive the expression for the moment of inertia of a uniform solid sphere of mass M and radius R about a diameter using integration. State the parallel-axis theorem and use it to find the moment of inertia about a tangent.
  • Q27. (4 marks) A disc of mass 2 kg and radius 0.5 m is rotating about its central axis at 10 rad/s. A second identical disc, initially at rest, is gently placed on top so that their axes coincide. Calculate the final angular velocity if they rotate together. State any law or principle used.
  • Q28. (5 marks) A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. Derive expressions for (i) its linear acceleration down the plane, and (ii) its speed at the bottom. Compare with the speed of a block sliding frictionlessly down the same incline.

Section F – Case Study Question (4 marks)

Read the scenario below carefully and answer the sub-questions that follow. Case-study questions integrate real-world contexts with physics principles and have become a staple of CBSE board papers since 2021. Marks are awarded for correct interpretation of data, application of formulae and logical reasoning. This case study ties together centre of mass, torque and rotational dynamics concepts from Chapter 6. Suggested time: 15 minutes. Write brief, precise answers; bullet points are acceptable if the question permits. Ensure dimensional consistency and quote any approximations made.

Complete Answer Key with Explanations

Below are the correct answers and brief explanations for all questions in this worksheet. Use this key for self-assessment and to identify areas needing revision. For numerical problems, intermediate steps are shown to help you trace errors in your working. Cross-reference with NCERT Class 11 Physics Chapter 6 textbook examples and solved problems. If a concept remains unclear after checking the key, consider joining CBSETUTOR.ai for instant photo-upload doubt solving and personalised video explanations at a flat ₹999/month across all subjects and classes (6–12), with a 3-day free trial to explore the platform risk-free.
  • Section A Answers: Q1–(B) m₂:m₁ | Q2–(B) ML²/3 | Q3–(C) 125% [KE ∝ L²; 1.5² = 2.25 → 125% increase] | Q4–(A) Solid sphere [smaller I → larger acceleration] | Q5–(C) 90° [sin90°=1 → max torque] | Q6–(B) 4:3 [KE=½Mv²(1+I/MR²); disc I=½MR², ring I=MR² → ratios 3/2: 2 = 3:4 is incorrect; correct ratio disc 3/4 v², ring 1 v² → 3:4 by velocity; by equal v it is 3/4:1= 3:4 wait recompute: KE_disc=½Mv²(1+½)=¾Mv², KE_ring=½Mv²(1+1)=Mv² → ratio 3:4 matches (A) but answer (B) given in some keys for same radius same v rolling; recheck NCERT: for same v, disc has less KE; correct answer is (A) 3:4]
  • Section B Answers: Q7–Newton-metre (N·m) | Q8–centre of mass | Q9–MR²/2 [perpendicular-axis theorem: I_z = I_x + I_y; for ring I_z=MR², by symmetry I_x=I_y → I_diameter=MR²/2] | Q10–planar | Q11–R [v=ωR]
  • Section C Part I Answers: 1–C | 2–A | 3–B | 4–D | 5–E
  • Section C Part II Answers: Q16–False [e.g. ring, hollow sphere] | Q17–True | Q18–False [I depends on axis] | Q19–True [I_solid_cyl=½MR² < I_hollow_cyl=MR²] | Q20–False [conserved only when net external torque is zero, not just force]
  • Section D Answers: Q21–The centre of mass is the point where the entire mass of the system can be considered concentrated for translational motion analysis. For two particles: X_cm=(m₁x₁+m₂x₂)/(m₁+m₂). | Q22–τ = r×F; r=(2,0,0), F=(10,0,0) ∴ τ=0 (parallel vectors, sin0°=0). | Q23–Perpendicular-axis theorem: For a planar body, I_z=I_x+I_y. For disc about central axis I_z=½MR²; by symmetry I_x=I_y ∴ I_diameter=¼MR². Wait, recheck: I_z perpendicular to plane = ½MR², I_x and I_y are diameters in plane, I_x=I_y, so ½MR²=2I_x → I_diameter=¼MR². Correct. | Q24–KE=KE_trans+KE_rot=½Mv² + ½Iω²; for solid sphere I=⅖MR², ω=v/R ∴ KE=½Mv²+½(⅖MR²)(v²/R²)=½Mv²+⅕Mv²= (7/10)Mv². | Q25–Radius of gyration k is the distance from the axis at which the entire mass, if concentrated, gives the same moment of inertia: I=Mk². It simplifies rotational inertia comparisons and depends on mass distribution and axis choice.
  • Section E Answers: Q26–Consider sphere of radius R. Take elemental disc at distance x from centre, thickness dx, radius y=√(R²−x²). dI=(½dm·y²)+(dm·x²) by parallel-axis theorem for disc. dm=ρπy²dx=(3M/4πR³)π(R²−x²)dx. Integrate dI from −R to +R: after integration I=(2/5)MR². By parallel-axis theorem about tangent: I_tangent=I_cm+MR²=(2/5)MR²+MR²=(7/5)MR². | Q27–Conservation of angular momentum: L_initial=I₁ω₁=½(2)(0.5)²(10)=2.5 kg·m²/s. Combined I=2×½MR²=MR²=2(0.5)²=0.5 kg·m². ω_final=L/I=2.5/0.5=5 rad/s. | Q28–For cylinder: mg sinθ − f = Ma; torque fR=Iα=½MR²(a/R) ∴ f=Ma/2. Substitute: mg sinθ − Ma/2=Ma → a=(2/3)g sinθ. At bottom: mgh=½Mv²+½Iω²=½Mv²(1+½)= (3/4)Mv² ∴ v=√(4gh/3). For frictionless block: v_block=√(2gh). Ratio v/v_block=√(2/3)≈0.816; cylinder slower.
  • Section F Answers: Q29a–At the geometric centre, 2.5 m from either end. | Q29b–Net torque about base point = 0; clockwise = anticlockwise. | Q29c–Torques about base (taking clockwise +ve): (20×10)(2.5 cos53°) + (60×10)(x cos53°) = N_wall(5 sin53°). Normal from wall N_wall = friction at base f = μN_ground. Vertical equilibrium: N_ground=80×10=800 N ∴ f=0.4×800=320 N. Torque balance: 200×2.5×0.6 + 600×x×0.6 = 320×5×0.8 → 300 + 360x = 1280 → x≈2.72 m. Painter can climb up to 2.72 m from bottom before slipping.

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Tips for Effective Worksheet Practice and Revision

To maximise learning from this System of Particles and Rotational Motion worksheet, follow a disciplined revision cycle. First, attempt all sections in one 90-minute sitting without referring to notes or solutions; this simulates exam pressure and reveals your current proficiency level. Next, use the answer key to score yourself honestly, noting not just wrong answers but also questions where you guessed or took excessive time. Identify recurring weak spots — perhaps perpendicular-axis theorem applications or angular-momentum conservation problems — and revisit those NCERT sections with fresh focus. Re-solve flagged questions after a day or two to reinforce correct methods. Maintain a separate error log in your Class 11 Physics notes: write down the mistake, the correct approach, and a one-line memory cue. For numerical problems, always write down known data, required quantity, relevant formula, substitution and final answer with units; this structured format mirrors CBSE step-marking and prevents careless errors. Finally, practice similar worksheets weekly, varying question styles and difficulty, to build speed and accuracy. Pair worksheet drills with conceptual video lessons on CBSETUTOR.ai for a balanced study plan that covers breadth (worksheets) and depth (doubt clarification). Consistent, reflective practice transforms mechanical problem-solving into deep conceptual mastery.
  • Simulate exam conditions: 90-minute timed attempt, no notes, no distractions.
  • Self-score using the answer key; track percentage and time per section for progress monitoring.
  • Maintain an error log: note the mistake, correct method and a memory cue for each wrong answer.
  • Revisit weak NCERT topics immediately; use Class 11 Physics solutions and example problems for reinforcement.
  • Re-attempt flagged questions after 24–48 hours to test retention and cement correct techniques.
  • Combine worksheet practice with video explanations on CBSETUTOR.ai for comprehensive concept clarity and exam readiness.

Frequently asked questions

What topics from System of Particles and Rotational Motion are covered in this worksheet?+
This worksheet comprehensively covers centre of mass, torque, angular momentum, moment of inertia (including parallel-axis and perpendicular-axis theorems), radius of gyration, and rolling motion — all core topics from NCERT Class 11 Physics Chapter 6 aligned with the CBSE 2025 syllabus.
How much time should I allocate to complete this Class 11 Physics Chapter 6 worksheet?+
The suggested time is 90 minutes for the entire worksheet. Section-wise: MCQs 12 min, fill-in-the-blanks 10 min, match/true-false 8 min, short answers 30 min, long HOTS 25 min, and case study 15 min. Strict timing builds exam discipline and speed.
Is the answer key provided with step-by-step explanations?+
Yes, a complete answer key with detailed explanations, formula applications and intermediate calculation steps is included at the end of the worksheet. This enables self-assessment, instant feedback and concept reinforcement without needing a teacher present.
What is the difficulty level of this worksheet — suitable for all students?+
The difficulty is moderate to challenging, designed for regular CBSE Class 11 students aiming for strong board exam performance and those preparing for competitive exams like JEE Mains. It balances recall-based questions with higher-order application and derivation problems.
Can I use this worksheet for quick revision before my term exam?+
Absolutely. The quick chapter recap, structured question sections and comprehensive answer key make this worksheet ideal for focused last-week revision. Time yourself to simulate exam conditions and identify weak areas for targeted study in the final days.
How does this worksheet align with the latest CBSE board exam pattern?+
The worksheet mirrors the 2025 CBSE board pattern with MCQs, short-answer questions (2–3 marks), long-answer HOTS questions (4–5 marks) and a case-study question. It follows NCERT terminology, mark distribution and question phrasing seen in recent board papers.
Where can I find additional doubt-solving support for tricky questions in this worksheet?+
CBSETUTOR.ai offers 24×7 AI-powered doubt solving with photo-upload capability. Upload any question from this worksheet and receive step-by-step video or text solutions instantly, all at a flat ₹999/month subscription with a 3-day free trial available.
Are there any case-study questions in this worksheet?+
Yes, Section F includes one comprehensive case-study question worth 4 marks. It integrates real-world scenarios — such as a ladder leaning against a wall — with centre of mass, torque and equilibrium concepts, reflecting the analytical skills tested in modern CBSE exams.
What formula sheet should I prepare before attempting this worksheet?+
Prepare a one-page formula sheet with centre of mass equations, torque τ=r×F, angular momentum L=Iω, moments of inertia for standard shapes (ring, disc, rod, sphere, cylinder), parallel-axis theorem I=I_cm+Md², perpendicular-axis theorem, rolling condition v=ωR, and kinetic energy expressions for rolling bodies.
Can this worksheet help me prepare for JEE Mains physics as well?+
Yes. System of Particles and Rotational Motion is a high-weightage topic in JEE Mains. The HOTS questions, derivations and multi-step numericals in this worksheet closely match JEE difficulty. Regular practice with detailed solutions builds the problem-solving speed and conceptual depth required for competitive exams.

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