MPH 2 Solved Guess Paper from Unnati Educations gives IGNOU M.Sc. Physics learners 12 high-probability questions from MPH-002 Classical Mechanics I, each answered the way examiners mark it. It is written for the December 2026 term-end exam, and five full answers are open below so you can check the quality first.
MPH-002 Classical Mechanics-I is the IGNOU course where Newton's force-by-force approach gives way to the Lagrangian method, central force orbits and small oscillations. Most learners understand the ideas well enough. Marks go missing in derivations that skip a line or stop without a conclusion, and that is the gap this paper closes.
MPH-002 key facts
- Course code: MPH-002
- Course title: Classical Mechanics-I
- Programme: M.Sc. Physics (MSCPH), IGNOU
- Blocks covered: 2: Lagrangian Formulation; Central Force and Small Oscillations
- Questions in the paper: 12 (10 five-mark parts and 2 ten-mark derivations)
- Sample answers on this page: 5 of 12
- Papers analysed: Five years of term-end papers, up to June 2026
- Built for: December 2026 term-end exam
- Format and language: PDF, English
- How to order: WhatsApp 9899436384
What the MPH 2 Solved Guess Paper Covers in Classical Mechanics I
The paper holds 12 MPH-002 questions: 10 five-mark answers and 2 ten-mark derivations, spread across both blocks of the course.
Nothing here is a random pick from the course. Each question was chosen because it keeps returning in MPH-002 papers or has been missing long enough to be due. This set is one part of our wider IGNOU Solved Guess Paper collection, where every course code gets its own questions instead of a recycled template.
| Q | Question topic | Block | Marks | Priority | Last appeared (Jun 2024 to Dec 2025) |
|---|---|---|---|---|---|
| 1 | Holonomic, non-holonomic, scleronomic and rheonomic constraints | Block 1 | 5 | High | Dec 2025, Jun 2025, Jun 2024 |
| 2 | D'Alembert's principle applied to an Atwood machine (M and 2M) | Block 1 | 5 | Medium | Dec 2024 |
| 3 | Hamilton's principle and derivation of the Euler-Lagrange equations | Block 1 | 10 | High | Not asked in the last four sessions (gap) |
| 4 | Lagrangian of a bead sliding on the parabola y = AxΒ² | Block 1 | 5 | High | Dec 2025, Jun 2025, Dec 2024 |
| 5 | Generalised momentum, cyclic coordinates and the energy function | Block 1 | 5 | High | Dec 2025, Jun 2025 |
| 6 | Elastic collision: vβ relation and right-angle separation for equal masses | Block 1 | 5 | High | All four sessions |
| 7 | Differential equation of the orbit in terms of u = 1/r | Block 2 | 5 | Medium | Dec 2024 |
| 8 | Effective potential and the nature of orbits for V = βk/r | Block 2 | 5 | High | Dec 2025, Jun 2025 |
| 9 | Kepler's third law, TΒ² β aΒ³, from constant areal velocity | Block 2 | 5 | Medium | Dec 2025 |
| 10 | Laplace-Runge-Lenz vector: definition, conservation, orbit plane | Block 2 | 5 | High | Dec 2025, Jun 2024 |
| 11 | Matrix theory of small oscillations and two coupled pendulums | Block 2 | 10 | High | All four sessions |
| 12 | Free damped oscillator: over, critical and under-damped cases | Block 2 | 5 | Medium | Dec 2024 |
Rows marked High either showed up in three or four of the last four sessions or have been absent long enough that a return is likely. Medium rows appeared once recently and still sit close to the core of Classical Mechanics I.
IGNOU MPH 2 Important Questions: 5 Sample Answers
Five of the twelve answers are shown below in full, exactly as they appear in the PDF, so you can check the depth before ordering.
The five answers mix both blocks and both mark levels: three 5-mark parts and two 10-mark derivations. Read them the way an examiner would and see whether every step earns its place.
Sample 1: Holonomic and Non-holonomic Constraints
Question: Define a constraint. Distinguish between holonomic and non-holonomic constraints with one example of each. Mention scleronomic and rheonomic constraints.
Meaning of a constraint
A constraint is a restriction that forces a system to move along a definite path or surface. The equations describing that path or surface are called constraint equations.
Holonomic and non-holonomic
- Holonomic: can be written as an equality f(rβ, β¦, rN, t) = 0 in coordinates (and possibly time), with no velocities. Example: the simple pendulum, xΒ² + yΒ² β LΒ² = 0.
- Non-holonomic: cannot be written as such an equality because it involves velocities or an inequality. Example: a disc rolling without slipping, dx = a cosΟ dΞΈ.
Scleronomic and rheonomic
Constraints with no explicit time dependence are scleronomic. Those that depend explicitly on time, such as a pendulum whose length changes as L = LβtΒ², are rheonomic.
Conclusion: holonomic constraints reduce the degrees of freedom and let us pick independent generalised coordinates; non-holonomic constraints cannot be removed this way.
Sample 2: Hamilton's Principle and the Euler-Lagrange Equations
Question: State Hamilton's principle (the principle of least action) for a dynamical system and use it to derive the Euler-Lagrange equations of motion.
Action and Hamilton's principle
Each configuration of a system is a point in n-dimensional configuration space, and its motion traces a path there. The action S is the time integral of the Lagrangian L = T β V along that path between tβ and tβ.
S = β«(tβ to tβ) L(qα΅’, qΜα΅’, t) dt
Statement: of all possible paths a system may take between two configurations in a given time, the actual path is the one for which the action is stationary.
Derivation
Hamilton's principle requires Ξ΄S = 0 for variations Ξ΄q that vanish at the end points. Varying the action gives:
Ξ΄S = β« [ (βL/βq) Ξ΄q + (βL/βqΜ) Ξ΄qΜ ] dt = 0
Write Ξ΄qΜ = d(Ξ΄q)/dt and integrate the second term by parts. The boundary term drops out because Ξ΄q = 0 at tβ and tβ, leaving:
Ξ΄S = β« [ βL/βq β d/dt (βL/βqΜ) ] Ξ΄q dt = 0
Since Ξ΄q is arbitrary between the end points, the bracket must vanish. This gives one equation for each generalised coordinate qj:
d/dt (βL/βqΜβ±Ό) β βL/βqβ±Ό = 0
Conclusion: these n second-order equations are the Euler-Lagrange equations. They hold for holonomic systems with forces derived from a potential, and they pack the whole dynamics into one scalar function, L.
Sample 3: Elastic Collision Between Two Particles
Question: A particle of mass mβ moving with velocity v collides elastically with a particle of mass mβ at rest. Using conservation laws, obtain vβ and show that for equal masses the particles separate at right angles.
Conservation laws
In an elastic collision, linear momentum and kinetic energy are both conserved. Resolving momentum along and perpendicular to the incident direction, with scattering angles ΞΈβ and ΞΈβ:
mβv = mβvβcosΞΈβ + mβvβcosΞΈβ ; 0 = mβvβsinΞΈβ β mβvβsinΞΈβ mβvΒ² = mβvβΒ² + mβvβΒ²
Squaring and adding the momentum equations to remove ΞΈβ, then using the energy equation, gives:
vβ = 2mβv cosΞΈβ / (mβ + mβ)
Equal masses (mβ = mβ)
Now vβ = v cosΞΈβ, and the relations reduce to tanΞΈβ = tan(90Β° β ΞΈβ), so ΞΈβ + ΞΈβ = 90Β°.
Conclusion: equal masses with one initially at rest always move apart at right angles after an elastic collision, a result used widely in scattering experiments.
Sample 4: Effective Potential and the Nature of Orbits
Question: Define the effective potential for a particle of mass m moving in a central force field with angular momentum l. Hence discuss the nature of orbits in an attractive inverse-square field.
Effective (fictitious) potential
Using conservation of angular momentum to eliminate Ο, the radial motion behaves like one-dimensional motion in an effective potential:
Vβ²(r) = V(r) + lΒ²/(2mrΒ²)
The added term lΒ²/(2mrΒ²) is the repulsive centrifugal contribution. Energy conservation reads E = Β½mαΉΒ² + Vβ²(r), so the particle can only reach regions where E β₯ Vβ²(r).
Attractive inverse-square field, V = βk/r
- E > 0: unbound hyperbolic orbit; the particle comes in to a minimum distance and escapes.
- E = 0: borderline unbound parabolic orbit.
- E < 0: bound elliptical orbit; r oscillates between two turning points.
- E = Vβ²min: circular orbit at the minimum of Vβ².
Conclusion: the effective potential turns a two-dimensional central force problem into a one-dimensional radial one, and E relative to Vβ² decides whether the orbit is bound.
Sample 5: Small Oscillations and Normal Modes of Coupled Pendulums
Question: Outline the matrix theory of small oscillations about stable equilibrium. For two identical pendulums of mass m and length l coupled by a spring of constant k, write the V and T matrices and obtain the normal-mode frequencies.
General theory
Near stable equilibrium the potential is a minimum. Writing small deviations Ξ·α΅’ = qα΅’ β qβα΅’ and expanding T and V to second order gives:
V = Β½ Ξ£ V(ij) Ξ·α΅’Ξ·β±Ό , T = Β½ Ξ£ T(ij) Ξ·Μα΅’Ξ·Μβ±Ό
Here Vij = (βΒ²V/βqα΅’βqj)β and Tij are constant symmetric matrices. Trying Ξ·j = ajeiΟt in Lagrange's equations gives (V β ΟΒ²T)a = 0, which has non-trivial solutions only when the secular determinant vanishes:
| V β ΟΒ²T | = 0
Two coupled pendulums
With displacements xβ and xβ, V = Β½(mg/l)xβΒ² + Β½(mg/l)xβΒ² + Β½k(xβ β xβ)Β² and T = Β½mαΊβΒ² + Β½mαΊβΒ². The matrices are:
V = [ (mg/l + k) βk ; βk (mg/l + k) ] , T = [ m 0 ; 0 m ]
The secular equation (mg/l + k β mΟΒ²)Β² β kΒ² = 0 gives the two normal frequencies:
Οβ = β(g/l) , Οβ = β(g/l + 2k/m)
Conclusion: Οβ is the in-phase mode, where the spring never stretches, and Οβ is the out-of-phase mode. Any motion of the system is a superposition of these two normal modes.
That is 5 answers out of 12. The other 7 cover D'Alembert's principle with the Atwood machine, the bead on a parabola, generalised momenta and the energy function, the orbit equation, Kepler's third law, the Laplace-Runge-Lenz vector and the damped oscillator. All 7 are in the complete PDF.
MPH 2 Classical Mechanics I Syllabus: Block and Unit Map
MPH-002 Classical Mechanics-I has two blocks: Block 1, The Lagrangian Formulation of Mechanics, and Block 2, Central Force and Small Oscillations.
The official course material is available on eGyanKosh, IGNOU's digital repository: see Block 1 on eGyanKosh and the Small Oscillations unit in Block 2. The table below maps each unit to the guess-paper questions drawn from it, so you can see where your revision time goes.
| Block | Unit | Key topics | Guess paper questions |
|---|---|---|---|
| Block 1 | Unit 1 | Newtonian mechanics revisited: equations of motion and conservation laws for one particle and many-particle systems | Q6 |
| Block 1 | Unit 2 | Constraints, generalised coordinates, virtual work and D'Alembert's principle | Q1, Q2 |
| Block 1 | Unit 3 | Lagrange's equations of motion and their use on bead, pendulum and pulley problems | Q4 |
| Block 1 | Unit 4 | Hamilton's principle, the action integral, cyclic coordinates and conservation theorems | Q3, Q5 |
| Block 2 | Unit 5 | Central force motion: radial equation, orbit equation and the effective potential | Q7, Q8 |
| Block 2 | Unit 6 | Inverse-square field: Kepler's laws, Laplace-Runge-Lenz vector and related theorems | Q9, Q10 |
| Block 2 | Unit 7 | Small Oscillations-I: stable equilibrium, T and V matrices, secular equation, normal modes | Q11 |
| Block 2 | Unit 8 | Oscillations with damping: equation of motion and the three damping regimes | Q12 |
If you are still working through the blocks, finish the unit reading with our MPH 2 Study Material first. Answer practice works far better once the notation in each unit feels familiar.
How the IGNOU MPH 2 Guess Paper Questions Were Picked
Every MPH-002 topic was tracked across five years of IGNOU term-end papers up to June 2026, then ranked by how often it repeats and how long it has been missing.
The starting point was simple: list every question asked in MPH-002 Part A, tag it to a unit, and count. Five years of papers were covered, and the December 2025 and June 2026 papers were read closely because they show where the examiners are heading now.
A few patterns stood out. Elastic collisions, Lagrange's equations and small oscillations appeared in every session from June 2024 to December 2025. Hamilton's principle did not appear once in those four papers, which is exactly why it is a 10-mark priority here rather than an afterthought.
Some topics were left out on purpose. The virial theorem showed up once in June 2024 and rigid-sphere scattering once in December 2024, so they did not earn a place ahead of topics that repeat. You can check these patterns yourself in our IGNOU Previous Year Question Paper section.
MPH-002 Exam Pattern and Answer Writing for Classical Mechanics I
In the papers we analysed, MPH-002 appears as a 25-mark Part A with internal choice in every question: three 5-mark questions and one 10-mark question.
In those papers, MPH-002 shares a 3-hour, 50-mark sitting with MPH-003 as Part B. Every question gives you a choice of two parts, so you never face a single topic you cannot avoid. Calculators are allowed.
That shared sitting matters for planning. If MPH-003 is on the same exam sheet for you, preparing both together with the matching MSCPH Guess Paper set saves you from building two separate revision plans.
When writing, open with the exact statement or definition and name the principle. Show the key steps of each derivation, because examiners reward the chain of logic, not only the final line. Pair the theory with its standard example and finish with one sentence on what the result means physically.
Who Should Order the MPH 2 Solved Guess Paper
It suits MSCPH learners sitting MPH-002 in December 2026 who understand the theory but lose marks when writing derivations under time pressure.
The paper is written for learners in IGNOU's M.Sc. Physics (MSCPH) who are short on time. Most are working, many are studying physics again after a gap of several years, and very few have a teacher to check their derivations.
It also helps if you are re-appearing in MPH-002, or if you have read the blocks but never timed yourself writing a 250-word derivation. What it will not do is replace the course material. It is a guess paper, not a leaked paper, and it works best on top of your own reading.
How to Get the Complete MPH 2 Guess Paper on WhatsApp
Message 9899436384 on WhatsApp with the course code MPH-002, confirm your session, and the full 12-answer PDF is shared after confirmation.
- Open WhatsApp and message 9899436384 with "MPH-002 guess paper".
- Tell the team your exam session so the right edition is shared.
- Get the price and payment details, and complete the payment.
- Receive the complete PDF with all 12 answers on the same chat.
The MPH 2 Solved Guess Paper is a digital PDF, so there is no shipping wait. If a derivation still confuses you after reading it, message the same number and the team will walk you through it.
MPH 2 Classical Mechanics I Guess Paper: FAQs
Quick answers to what MSCPH learners ask most before ordering the MPH-002 guess paper.
Is the MPH 2 guess paper enough to pass Classical Mechanics I?
It is built to carry most of your Part A preparation, not to replace the course. The 12 questions cover the topics that repeat most in MPH-002, with full derivations and conclusions. Read the related units once, then practise these answers in your own handwriting. Learners who do both usually walk in knowing exactly what to write. No guess paper can promise the exact questions, though.
How many questions does the IGNOU MPH 2 guess paper contain?
The IGNOU MPH 2 guess paper contains 12 questions with complete answers. Ten are 5-mark parts of about 150 words and two are 10-mark derivations of about 250 words: Hamilton's principle and the coupled pendulum normal modes. Five of the twelve answers are shown on this page as samples, and the remaining seven are in the PDF you receive on WhatsApp.
Which MPH 2 topics are most likely in the December 2026 exam?
Elastic collisions, Lagrangian equations of motion and small oscillations with normal modes appeared in every MPH-002 paper from June 2024 to December 2025. Constraints, the effective potential and generalised momenta also repeat often. Hamilton's principle has not been asked in those four sessions, which is why it is treated as a high-priority 10-mark question in the guess paper for December 2026.
Are the MPH 2 answers based on the IGNOU MPH-002 study material?
Yes. Every answer in the MPH 2 guess paper follows the IGNOU MPH-002 self-learning material: the same notation, the same standard examples and the same order of derivation used in Block 1 and Block 2. That matters because examiners check your working against the course text. Nothing is borrowed from unrelated textbooks that use different symbols or skip IGNOU's steps.
Can I see MPH 2 Classical Mechanics I answers before ordering?
Yes. Five complete MPH 2 Classical Mechanics I answers are published on this page: constraints, Hamilton's principle, elastic collision, effective potential and coupled pendulums. They let you judge the language, depth and layout before you spend anything, so you know exactly what the other seven answers will look like.
How do I get the full MPH 2 guess paper PDF?
Send a WhatsApp message to 9899436384 mentioning MPH-002 and your exam session. The Unnati Educations team confirms the edition, shares the price and payment details, and sends the complete MPH 2 guess paper PDF once payment is confirmed. The same number handles doubts after you receive the file, so you are not left alone with a derivation that does not make sense.
Will the MPH 2 guess paper help for the June 2027 exam as well?
Most of it, yes. MPH-002 keeps returning to the same core areas: Lagrangian mechanics, central force orbits and small oscillations. The priority order can shift after each new paper, though. If you are sitting June 2027, message 9899436384 before ordering and ask whether an updated MPH 2 edition with the December 2026 paper analysed is available.