BPHCT 131 Solved Question Paper for June 2026 gives you complete, exam-length answers to the IGNOU Mechanics Term-End paper set for B.Sc. (General) and B.Sc. (Multidisciplinary) students. Two answers are open on this page so you can judge the quality, and the full file with every part solved comes on WhatsApp 9899436384.
BPHCT 131 Mechanics June 2026 key facts
- Course code: BPHCT-131
- Subject: Mechanics
- Programme: Bachelor of Science (General) BSCG and Bachelor of Science (Multidisciplinary) BSCM
- Credits: 4 (theory), Semester 1 as listed by IGNOU; lab course BPHCL-132 carries 2 more
- Blocks / units: 4 blocks: Mathematical Preliminaries; Basic Concepts of Mechanics; Rotational Motion and Many-Particle Systems; Harmonic Oscillations. Units: [VERIFY]
- Maximum marks: 50
- Duration: 2 hours
- Questions in the paper: 5 compulsory questions with 20 printed parts (attempt 13)
- Samples shown on this page: 2 (Q2(a) and Q4(b))
- Questions in the paid file: All 20 parts solved, 18 of them not shown on this page
What the BPHCT 131 Solved Question Paper June 2026 covers
BPHCT 131 Mechanics is a 4-credit Semester 1 physics core theory course of IGNOU's B.Sc. (General) and B.Sc. (Multidisciplinary) programmes, and this file solves its June 2026 paper part by part.
The official IGNOU BPHCT 131 Question Paper for June 2026, printed as Aโ1455, tests vectors, differential equations, Newtonian dynamics, rotation, gravitation, oscillations and waves in one sitting. The IGNOU BPHCT 131 Solved Question Paper from Unnati Educations answers all 20 printed parts, so whichever five short parts and eight long parts you would have picked, the worked solution is there.
Several parts are close repeats of older papers. The bicycle question in Q1(c) reuses the December 2025 set-up with 180 m in place of 150 m, the spring-force work in Q1(d) uses the same F = โax โ bx2 form seen in December 2022, and the damped equation in Q5(b) follows the December 2022 format with new numbers.
If you want those earlier papers side by side with this one, our IGNOU Previous Year Question Paper collection keeps them in one place, sorted by course code and session.
BPHCT 131 Mechanics sample answers: two parts solved in full
Two complete answers are shown below, Question 2(a) on uniform circular motion and Question 4(b) on the collapsing star, and the remaining 18 parts are listed exactly as printed, with answers only in the full file.
Both samples are 5-mark answers, the length IGNOU expects in Questions 2 to 5. They were written by our subject team for this page, since the official paper carries questions only.
Question 2(a) [5 marks]
For the uniform circular motion of a particle show that : (i) the velocity of the particle is perpendicular to the position vector at each instant of time. (ii) the acceleration of the particle is perpendicular to its velocity.
Answer. Let the particle move on a circle of radius R centred at the origin with constant angular speed ฯ. Its position vector at time t is rโ(t) = R cos ฯt รฎ + R sin ฯt ฤต, so |rโ| = R stays fixed for all t.
(i) Velocity is perpendicular to the position vector. Differentiating, vโ = drโ/dt = โRฯ sin ฯt รฎ + Rฯ cos ฯt ฤต. The scalar product is rโยทvโ = (R cos ฯt)(โRฯ sin ฯt) + (R sin ฯt)(Rฯ cos ฯt) = 0. Neither vector is zero, so a zero scalar product means vโ โฅ rโ at every instant.
The same result follows without components. Since rโยทrโ = R2 is constant, d/dt (rโยทrโ) = 2 rโยท(drโ/dt) = 2 rโยทvโ = 0. Hence rโยทvโ = 0 for any motion at constant distance from the centre, and the velocity is always tangential.
(ii) Acceleration is perpendicular to velocity. Differentiating again, aโ = dvโ/dt = โRฯ2 cos ฯt รฎ โ Rฯ2 sin ฯt ฤต = โฯ2 rโ. Then vโยทaโ = (โRฯ sin ฯt)(โRฯ2 cos ฯt) + (Rฯ cos ฯt)(โRฯ2 sin ฯt) = 0, so aโ โฅ vโ.
In uniform circular motion the speed is constant, so vโยทvโ = R2ฯ2 does not change with time. Differentiating gives 2 vโยท(dvโ/dt) = 2 vโยทaโ = 0, which confirms the result in general form.
Conclusion. The velocity has magnitude Rฯ and points along the tangent. The acceleration aโ = โฯ2 rโ has magnitude Rฯ2 = v2/R and points towards the centre. It is the centripetal acceleration, and it changes only the direction of motion, never the speed.
Question 4(b) [5 marks]
A star having rotational inertia of 8.6 ร 1048 kg m2 is rotating at an angular speed of 1 revolution per month about its axis. The only force on it is the force of gravitation. When its nuclear fuel is exhausted, it shrinks to a neutron star having rotational inertia of 4.5 ร 1037 kg m2. Determine the angular speed of the neutron star in revolution per month.
Answer. Given: initial rotational inertia I1 = 8.6 ร 1048 kg m2, initial angular speed ฯ1 = 1 revolution per month, final rotational inertia I2 = 4.5 ร 1037 kg m2. Required: final angular speed ฯ2 in revolutions per month.
Principle. The only force acting is the star's own gravitation. These are internal forces between pairs of particles, acting along the lines joining them, so they produce no net torque about the rotation axis. With zero net external torque, angular momentum L = Iฯ is conserved during the collapse.
Calculation. I1ฯ1 = I2ฯ2, so ฯ2 = (I1/I2) ฯ1 = (8.6 ร 1048 / 4.5 ร 1037) ร 1 rev/month = 1.91 ร 1011 rev/month. Because the ratio is taken directly, the unit of ฯ does not need converting.
Sense check. Taking a 30-day month of 2.592 ร 106 s, this is about 7.4 ร 104 revolutions per second, which shows why collapsed stars spin extremely fast. Rotational kinetic energy L2/2I rises by the same factor of 1.91 ร 1011, with the extra energy coming from gravitational potential energy released in the collapse.
Final answer. The neutron star rotates at about 1.9 ร 1011 revolutions per month.
Questions answered only in the full file
The 18 parts below appear exactly as printed in the June 2026 paper. Their worked answers are in the full solved file only.
- Q1(a) The magnitude of vectors pโ and qโ are 2 units and 3 units respectively and the value of pโยทqโ = 6. Calculate the angle between the two vectors. [2 marks]
- Q1(b) State the order and degree of the following differential equation : (yโณ)2 = 1 + (yโฒ)3 [2 marks]
- Q1(c) A bicycle travels 180 m along a circular track of radius 15 m. What is the angular displacement in radians of the bicycle from its starting position ? [2 marks]
- Q1(d) The one-dimensional restoring force exerted by a spring is given by F = โ ax โ bx2 where โaโ and โbโ are constants. Calculate the work done by the spring force in moving a mass โmโ from the point x = 0 to x = 1. [2 marks]
- Q1(e) What is the torque on the Earth due to the force of gravitation exerted by the Sun on it as it goes around the Sun in a nearly circular orbit ? [2 marks]
- Q1(f) Halleyโs comet moves in an elliptical orbit of eccentricity 0.967 about Sun. The length of orbitโs semi-major axis is 2.7 ร 1012 m. Determine the distance of Halleyโs comet from the Sun at perihelion. [2 marks]
- Q1(g) An object of mass 0.5 kg is executing simple harmonic motion. Its amplitude is 20 cm and period is 0.1 s. Calculate the potential energy of the object when it is 5 cm from equilibrium position. [2 marks]
- Q1(h) A particle is simultaneously subjected to two mutually perpendicular oscillations given by : x = 4 sin t cm, y = 4 cos t cm. Determine the trajectory of its motion. [2 marks]
- Q2(b) Write the first order ODE for the current I in a series LR circuit with a voltage source E sin ฯt and solve it to determine I as a function of time. [5 marks]
- Q2(c) Solve the following boundary value problem : yโณ โ 6yโฒ + 9y = 0; y(0) = 0, y(1) = 2 [5 marks]
- Q3(a) When a child pushes a carrom board striker of mass 20 g, it moves on the board in a straight line with initial speed of 1.5 msโ1. A constant force of friction F = 0.04 N is exerted opposite to the motion of the striker. How far will the striker move before it comes to rest ? [5 marks]
- Q3(b) A bucket of water of mass 3.0 kg is tied to a mass-less rope and whirled in a vertical circle with radius of 1.0 m. At the top of the circular loop, the speed of the bucket is 4.5 msโ1. Determine the tension in the string when bucket is at the top of the circular loop. Take g = 10 msโ1. [5 marks]
- Q3(c) A car of mass 2000 kg is travelling due west at a speed of 72 km hโ1. It comes to a stop in 10 s when the driver applies brakes. Determine the average force. [5 marks]
- Q4(a) (i) The average angular acceleration of a stone lodged in rotating car wheel is 50 rad. sโ2. What will be stoneโs final angular speed after 3.0 s if it starts from rest ? (2) (ii) A ball has angular velocity of 8.0 rad. sโ1 clockwise. After the ball rotates by an angle of 4.0 rad, it has angular velocity of 2.0 rad sโ1 clockwise. Determine the angular acceleration of the ball and time it takes to attain this angular velocity. (3) [5 marks]
- Q4(c) For a two-particle system with zero net external force, derive the equations of motion in terms of the relative and centre of mass coordinates. What is the reduced mass ? (4+1) [5 marks]
- Q5(a) The period of a simple pendulum is 4 s and its amplitude is 6ยบ. After 20 oscillations, its amplitude decreases to 3ยบ. Calculate the logarithmic decrement and damping factor. Also calculate the number of oscillations in which its amplitude reduces by 25%. [5 marks]
- Q5(b) The equation of motion of an oscillating body of mass 0.5 kg is : d2x/dt2 + 6 dx/dt + 9x = 0, Calculate the force constant โkโ, the angular velocity ฯ0, the damping constant โฮณโ and the damping factor. [5 marks]
- Q5(c) (i) Sound propagates in air with a speed of 332 msโ1. The audible range lies between 20Hz to 20 kHz. Calculate the corresponding wavelengths. (2) (ii) A tidal wave having a maximum height of 5.0 m propagating in the โve Xโdirection with a speed of 90 msโ1 can be approximated by a sine function. The distance between two successive crests is 5 m. Write the expression for the wave. (3) [5 marks]
BPHCT 131 question paper pattern and marks distribution
The BPHCT 131 question paper for June 2026 carries 50 marks in 2 hours, with five compulsory questions, 20 printed parts and 13 parts to answer.
| Question | Parts printed | Parts to answer | Marks per part | Marks | June 2026 themes |
|---|---|---|---|---|---|
| Question 1 | 8 | 5 | 2 | 10 | Vectors, ODE order, bicycle track, spring force, Earth's torque, Halley's comet, SHM energy, perpendicular oscillations |
| Question 2 | 3 | 2 | 5 | 10 | Circular-motion proof, LR circuit ODE, repeated-root boundary value problem |
| Question 3 | 3 | 2 | 5 | 10 | Carrom striker with friction, bucket in a vertical circle, braking car |
| Question 4 | 3 | 2 | 5 | 10 | Angular acceleration of a wheel stone and a ball, collapsing star, two-body reduction |
| Question 5 | 3 | 2 | 5 | 10 | Damped pendulum, damped oscillator equation, sound and tidal waves |
| Total | 20 | 13 | 2 or 5 | 50 | Every block of the course is tested |
The short parts in Question 1 reward quick, exact working, while Questions 2 to 5 expect a derivation or a full numerical of about one page each. The paper allows a calculator, which matters for the orbit and damping parts.
The Term-End paper is only part of your course result. IGNOU's BPHCT-131 assignment booklet gives the tutor-marked assignment a 30 per cent weightage, so this written exam decides the remaining share.
Students in either programme can compare this layout with other first-year science papers in our BSCG Question Paper set.
BPHCT 131 Mechanics syllabus mapped to the June 2026 paper
BPHCT 131 Mechanics has 4 blocks, and the June 2026 paper tests all of them across nine topic areas, from vectors and ODEs to damped oscillations and waves.
| Block | Topic area | Topics tested | June 2026 parts |
|---|---|---|---|
| Block 1: Mathematical Preliminaries | Vectors | Scalar and vector products, angle between vectors, torque as rโ ร Fโ | Q1(a), Q1(e) |
| Block 1: Mathematical Preliminaries | Ordinary differential equations | Order and degree, first-order linear ODEs with an integrating factor, constant-coefficient second-order boundary value problems | Q1(b), Q2(b), Q2(c) |
| Block 2: Basic Concepts of Mechanics | Motion and Newton's laws | Position-vector description of circular motion, kinetic friction, impulse and average force | Q2(a), Q3(a), Q3(c) |
| Block 2: Basic Concepts of Mechanics | Work, energy and circular dynamics | Work by a position-dependent force, work-energy theorem, tension at the top of a vertical loop | Q1(d), Q3(b) |
| Block 3: Rotational Motion and Many-Particle Systems | Rotational motion | Angular displacement from arc length, uniform angular acceleration, conservation of angular momentum | Q1(c), Q4(a), Q4(b) |
| Block 3: Rotational Motion and Many-Particle Systems [VERIFY] | Gravitation and central forces | Kepler's laws, eccentricity and perihelion distance, zero torque under a central force | Q1(e), Q1(f) |
| Block 3: Rotational Motion and Many-Particle Systems | Many-particle systems | Centre of mass coordinate, relative coordinate, reduced mass of a two-body system | Q4(c) |
| Block 4: Harmonic Oscillations | Oscillations | Potential energy in SHM, perpendicular superposition, damped motion and logarithmic decrement | Q1(g), Q1(h), Q5(a), Q5(b) |
| Block 4: Harmonic Oscillations [VERIFY] | Waves | Speed, frequency and wavelength of sound, sine-wave expression for a wave moving along โx | Q5(c) |
The mathematical tools (vectors and ODEs) carry real weight here: at least four of the 20 parts, Q1(a), Q1(b), Q2(b) and Q2(c), turn mainly on vector or ODE methods.
For unit-wise reading before the exam, use our BPHCT 131 Study Material alongside the official course blocks.
Most repeated BPHCT 131 Important Questions topics since June 2022
Kepler's laws and orbits appeared in all 7 official BPHCT 131 papers we checked, making gravitation the most reliable topic in this course.
We read these official papers from IGNOU's question paper archive: June 2022, December 2022, June 2023, December 2023, June 2024, June 2025 and December 2025. The December 2024 paper is listed on ignou.ac.in but its file is a scan we could not read reliably, so it is left out of the count.
| Topic | Sessions where it appeared | Count (of 7) | June 2026 part |
|---|---|---|---|
| Kepler's laws, orbits and satellites | June 2022, December 2022, June 2023, December 2023, June 2024, June 2025, December 2025 | 7 | Q1(e), Q1(f) |
| Angular kinematics of wheels, bicycles and grinding stones | June 2022, December 2022, June 2024, June 2025, December 2025 | 5 | Q1(c), Q4(a) |
| Travelling waves: wavelength, frequency, direction | June 2023, December 2023, June 2024, June 2025, December 2025 | 5 | Q5(c) |
| Boundary value problems (second-order ODE) | June 2022, December 2022, June 2023, December 2023 | 4 | Q2(c) |
| Order, degree and classification of an ODE | June 2022, June 2023, June 2024, December 2025 | 4 | Q1(b) |
| Amplitude decay, logarithmic decrement, relaxation time | December 2023, June 2024, June 2025, December 2025 | 4 | Q5(a) |
| Conservation of angular momentum when rotational inertia changes | December 2022, June 2023, December 2023, December 2025 | 4 | Q4(b) |
| Reduced mass, centre of mass and relative coordinates | June 2022, December 2022, June 2023, June 2025 | 4 | Q4(c) |
| Friction problems (stopping, inclines, static friction) | June 2022, December 2023, June 2024, June 2025 | 4 | Q3(a) |
| Damped oscillator equation: k, ฯโ, ฮณ, damping factor | June 2022, December 2022, December 2023 | 3 | Q5(b) |
| Tension in a vertical circle | December 2022, June 2024, June 2025 | 3 | Q3(b) |
| Circuit ODEs (LR or LCR) | June 2022, June 2025, December 2025 | 3 | Q2(b) |
| Circular motion from a position vector | June 2023, December 2023, December 2025 | 3 | Q2(a) |
| Superposition of perpendicular oscillations | December 2023, June 2024, June 2025 | 3 | Q1(h) |
| Energy in simple harmonic motion | December 2022, June 2023, December 2023 | 3 | Q1(g) |
| Impulse and average force | June 2022, June 2023, June 2024 | 3 | Q3(c) |
| Scalar and vector products of two vectors | June 2022, June 2023, December 2025 | 3 | Q1(a) |
| Work done by a variable force | December 2022, June 2023 | 2 | Q1(d) |
Almost every June 2026 part maps to a topic seen at least twice before. That is why a solved recent paper is worth more for BPHCT 131 than for most theory-heavy courses.
For predicted questions across other courses as well, see our IGNOU Important Questions page.
BPHCT 131 solved file index for all 20 parts
The full file solves all 20 parts; 2 are open on this page and 18 are in the full file only.
| Part | Topic | Marks | Where to find the answer |
|---|---|---|---|
| Q1(a) | Vectors: scalar product | 2 | Full file only |
| Q1(b) | Order and degree of an ODE | 2 | Full file only |
| Q1(c) | Angular displacement | 2 | Full file only |
| Q1(d) | Work by a variable force | 2 | Full file only |
| Q1(e) | Torque under a central force | 2 | Full file only |
| Q1(f) | Elliptical orbits and perihelion | 2 | Full file only |
| Q1(g) | Energy in SHM | 2 | Full file only |
| Q1(h) | Perpendicular oscillations | 2 | Full file only |
| Q2(a) | Uniform circular motion with vectors | 5 | On this page |
| Q2(b) | First-order ODE: LR circuit | 5 | Full file only |
| Q2(c) | Boundary value problem | 5 | Full file only |
| Q3(a) | Friction and stopping distance | 5 | Full file only |
| Q3(b) | Tension in a vertical circle | 5 | Full file only |
| Q3(c) | Impulse and average force | 5 | Full file only |
| Q4(a) | Angular kinematics | 5 | Full file only |
| Q4(b) | Conservation of angular momentum | 5 | On this page |
| Q4(c) | Two-particle system and reduced mass | 5 | Full file only |
| Q5(a) | Logarithmic decrement | 5 | Full file only |
| Q5(b) | Damped oscillator constants | 5 | Full file only |
| Q5(c) | Wavelength and wave equation | 5 | Full file only |
How our BPHCT 131 Mechanics answers are written and checked
Every BPHCT 131 answer is written to the marks printed against it, then recalculated and checked by a second reviewer before release.
Two-mark parts get a short, exact solution: the formula, the substitution and the final value with its unit. Five-mark parts get a full answer of about one page, with the given data listed, the governing law named and every step shown, as in the two samples above.
Derivations follow the vector methods IGNOU itself uses in this course, such as the derivative of a scalar product, which the December 2023 paper asked for by name. Numericals keep sensible significant figures and end with a sense check, like the revolutions-per-second check in Q4(b).
Prateek Talwar leads the writing and Sheetal Kirola reviews each file. Wherever a printed value looks inconsistent, the answer works with the physically correct unit and says so, rather than silently changing the question.
Programmes that include BPHCT 131 Mechanics
BPHCT 131 Mechanics is taught in IGNOU's B.Sc. (General) and B.Sc. (Multidisciplinary) programmes, and both sat the same June 2026 paper.
In the Bachelor of Science (General) programme (BSCG), IGNOU lists BPHCT-131 as a 4-credit Semester 1 theory course, paired with BPHCL-132 Mechanics: Laboratory worth 2 credits. Physics students meet it alongside BPHCT-133 Electricity and Magnetism in the same semester.
Bachelor of Science (Multidisciplinary) learners (BSCM) take the same course. IGNOU issued a BSCM assignment booklet for BPHCT-131 in 2024, and the June 2025, December 2025 and June 2026 papers print BSCG and BSCM together on the cover.
You can confirm the course listing and credits on IGNOU's official BSCG programme page.
Get the full BPHCT 131 Solved Question Paper on WhatsApp
Send "BPHCT 131 June 2026" on WhatsApp 9899436384 and you receive the full solved file with all 20 parts answered.
The file contains the 2 answers you have read here plus the 18 that are locked on this page, including the LR circuit, the boundary value problem, the two-body derivation and both damping numericals. Our team replies with the price and sends the PDF on the same chat.
BPHCT 131 Mechanics FAQs
These answers cover the questions BPHCT 131 Mechanics students ask most often about this solved paper.
How many answers are in the full BPHCT 131 Mechanics solved file and how do I get it?
Message WhatsApp 9899436384 with the code BPHCT 131 and the session June 2026, and our team replies with the price and the PDF. The full file solves all 20 printed parts of the paper, that is the eight short parts of Question 1 and the twelve longer parts of Questions 2 to 5. Two of those answers are already on this page, so the file adds 18 more.
Is the BPHCT 131 question paper the same for BSCG and BSCM students?
Yes. The June 2026 Term-End paper prints both programme codes, BSCG and BSCM, on its cover, so students of B.Sc. (General) and B.Sc. (Multidisciplinary) sat the same Mechanics paper. The June 2025 and December 2025 papers carried the same joint header. Earlier papers, such as June 2023 and June 2024, printed BSCG alone, before the multidisciplinary code was added to the cover.
How is the BPHCT 131 Mechanics paper of June 2026 structured?
The paper carries 50 marks over 2 hours and has five compulsory questions with internal choice. Question 1 offers eight 2-mark parts, of which you answer any five. Questions 2, 3, 4 and 5 each offer three 5-mark parts, of which you answer any two. In all you write 13 answers out of 20 printed parts, and a calculator is allowed in the hall.
Which BPHCT 131 topics repeat most in past Mechanics papers?
Kepler's laws, orbits and satellite questions appeared in all seven earlier papers we checked, from June 2022 to December 2025. Angular kinematics of wheels and bicycles appeared in five, and so did travelling-wave questions. Boundary value problems, order and degree of ODEs, amplitude decay, reduced mass, friction and conservation of angular momentum each appeared in four of those seven papers.
Are the BPHCT 131 sample answers written in IGNOU exam format?
Yes. Each answer lists the given data in SI units, names the law or result it relies on, shows every algebraic step and ends with a clear final value and unit. Derivations such as Question 2(a) use position vectors and the derivative of a scalar product, the same method the December 2023 BPHCT 131 paper asked for. Every numerical is recalculated before release.
Can the BPHCT 131 solved paper help with the December 2026 Mechanics exam?
It helps because BPHCT 131 papers recycle question types closely. The June 2026 bicycle question mirrors one from December 2025 with 180 m in place of 150 m, and the spring-force work question uses the same F = โax โ bxยฒ form set in December 2022. Practising the full solved file trains you on exactly these patterns before your next Term-End Examination.
Does the BPHCT 131 file cover the Mechanics laboratory course BPHCL 132?
No. BPHCL 132 Mechanics: Laboratory is a separate 2-credit course, and it is not examined in this written paper. This file covers only the BPHCT 131 theory paper of June 2026, which is a 4-credit course in its own right. If you also need help connected with BPHCL 132, mention it on WhatsApp 9899436384 and our team will tell you what is available.
Who wrote and checked the BPHCT 131 Mechanics answers?
The answers were prepared by the Unnati Educations team under author Prateek Talwar and reviewed by Sheetal Kirola before release. Every numerical answer was recalculated independently, units were checked against SI conventions, and each derivation was matched against the exact wording of the June 2026 question so that nothing the examiner asked for is left out of the answer.