IPhO Practice Test Questions 2025 | International Physics Olympiad Exam Papers

Practice free online IPhO Questions: Download solved (International Physics Olympiad) Exam Papers in PDF.

IPhO - Practice Mock Tests

Download IPhO Exam Papers (1967 - 2025) with Solutions [PDF]

Features:

• 📘 Year-wise IPhO Problems & Solutions
• 🌍 Host Country Context for Each Year
• 🔬 Categorized: Theory & Experimental
• 🆓 100% Free Download (PDF format)

✅ Click here to download previous year's (1967 - 2025) IPhO questions papers with solutions in PDF.

✅ Click here to download topic-wise IPhO questions with solutions in PDF.

Note: The list includes exam papers till 2024 (given below), but if the 2025 IPhO paper is officially released, you can download it here as soon as it's available.

Sample Questions for IPhO 2025

We have prepared a list of some application-based questions from following topics:

• Mechanics
• Electromagnetism
• Thermodynamics
• Fluid Dynamics
• Quantum Mechanics

The following questions are not official IPhO problems but are designed to help you understand the exam format and the level of difficulty.

Disclaimer: Testmocks is not affiliated with the IPhO and does not guarantee that these questions will appear in the actual competition.

🚀 Question 1: Rotating Rod and Relativistic Particle Collision

A uniform thin rod of length \( L \) and mass \( M \) is hinged at one end and can rotate freely in a vertical plane without friction. The rod is initially at rest in a horizontal position.

A particle of mass \( m \) is moving horizontally with a speed \( v \) and strikes the free end of the rod elastically. Assume the collision is instantaneous and the particle moves along the same line after the collision.

Additional Constraint: The mass of the particle is comparable to the rod (\( m \sim M \)), and the speed \( v \) is a significant fraction of the speed of light (i.e., relativistic effects must be considered).

Tasks:

1. Derive the expression for the angular velocity \( \omega \) of the rod immediately after the collision, considering conservation of both angular momentum and relativistic energy.
2. Express your answer in terms of \( M, m, L, v \), and \( c \) (speed of light), where necessary. Use the relativistic energy and momentum for the incoming particle:
   • \( E = \gamma mc^2 \)
   • \( p = \gamma mv \)
   • \( \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} \)
3. Determine the final velocity \( v' \) of the particle after the collision in the lab frame.

Note:

• Neglect gravitational effects during the collision.
• Moment of inertia of a rod about one end: \( I = \frac{1}{3}ML^2 \)

This problem involves combining classical rotational dynamics with relativistic linear momentum — a challenge designed to test creativity, synthesis of concepts, and mathematical skill.

🌀 Question 2: Tensioned Rod and Sliding Mass on a Rotating Platform

A smooth horizontal circular platform of radius \( R \) rotates with a constant angular velocity \( \omega \) about its vertical axis. A light, inextensible rod of length \( L < R \) is hinged at the center of the platform and lies flat on its surface. A small block of mass \( m \) is attached to the free end of the rod and can slide along the rod without friction. The rod can also rotate freely about its hinge, but always remains within the plane of the platform. There is no friction between the block and the rod.

At time \( t = 0 \), the block is held at the midpoint of the rod and released from rest relative to the rotating platform.

Tasks:

1. Derive the equations of motion of the block in the rotating frame using non-inertial forces (Coriolis and centrifugal forces). Express the motion in terms of the distance \( r(t) \) of the block from the center.
2. Find the general solution for \( r(t) \), assuming small initial displacement from the center. Identify the type of motion (oscillatory, unbounded, etc.) depending on \( \omega \).
3. Now consider the inertial (lab) frame. Using conservation of angular momentum, derive the effective force acting on the block and re-derive the trajectory \( r(t) \). Verify consistency with the rotating frame approach.
4. Finally, determine the normal force acting on the block from the surface of the platform during its motion.

Note:

• The rod does not exert any force except along its length (i.e., no torque).
• Neglect air resistance and assume the block remains in contact with the platform at all times.

This question challenges you to apply conservation laws in a rotating system. It requires a deep understanding of dynamics and the ability to switch between frames of reference, non-inertial dynamics, angular momentum conservation, and rotational constraint forces — a full workout for Olympiad-level understanding of mechanics.

⚡ Question 3: Inductive Mass Oscillation in a Magnetic Loop

A thin, flexible wire of length \( L \), mass per unit length \( \lambda \), and resistance \( R \), is formed into a semicircular arc of radius \( R_0 \), and connected to fixed conducting rails forming a complete circular loop. The system lies in a vertical plane and carries a steady current \( I \) powered by an external battery.

Due to gravity, the wire sags downward slightly, and begins to oscillate about its equilibrium position under the combined effects of tension and self-induced magnetic forces.

Tasks:

1. Derive the equation of motion of a small transverse element \( y(\theta, t) \), where \( \theta \in [0, \pi] \) is the angular coordinate along the wire. Include gravitational and magnetic contributions using the Biot–Savart law.
2. Linearize the equation for small oscillations, and find the normal modes of vibration. Show that the eigenfrequencies are modified due to magnetic tension and derive the leading correction term.
3. Estimate the total mechanical energy of the system stored in the lowest mode, and how it varies over time. Assume sinusoidal motion and compute the average power dissipated by Joule heating over one period.

Use the identity:

\[ \int_0^{\pi} \sin(n\theta)\sin(m\theta)\,d\theta = \begin{cases} 0 & n \ne m \\ \frac{\pi}{2} & n = m \end{cases} \] as needed for mode decomposition.

The IPhO often includes problems like this to test the understanding of oscillations in non-trivial systems, and the interplay between electric and magnetic forces - it tests the ability to linearize complex equations and find physical interpretations of the results.

🌡️ Question 4: Quantum Heat Engine with Discrete Spectrum

A single quantum particle of mass \( m \) is trapped in a 1D infinite potential well of width \( L \). Its energy levels are given by: \[ E_n = \frac{n^2 \pi^2 \hbar^2}{2mL^2}, \quad n = 1, 2, 3, \ldots \] The system is connected alternately to two heat reservoirs at temperatures \( T_H \) and \( T_C \) (with \( T_H > T_C \)), allowing it to undergo a Stirling-like thermodynamic cycle: isothermal expansion, isoenergetic compression, etc.

Tasks:

1. Derive an expression for the partition function \( Z(L, T) \) of the quantum system assuming it is in thermal equilibrium with a reservoir at temperature \( T \). Use the approximation: \[ Z(L, T) \approx \sum_{n=1}^{\infty} e^{- \beta E_n } \approx \int_0^\infty e^{- \beta \frac{n^2 \pi^2 \hbar^2}{2mL^2}}\,dn \] and evaluate the integral.
2. Find the internal energy \( U(T, L) \) and pressure-like quantity \( \left( \frac{\partial U}{\partial L} \right)_T \). Interpret this in terms of mechanical work when \( L \) is varied.
3. Compute the total work done and heat absorbed during one complete cycle. Compare the efficiency with Carnot efficiency and discuss the limiting behavior as \( T_H \to \infty \).

Useful result:

\[ \int_0^{\infty} e^{-a n^2} dn = \frac{1}{2} \sqrt{\frac{\pi}{a}}, \quad a > 0 \]

What a great way to explore the quantum world and its implications for macroscopic systems! This question is designed to challenge students' understanding of quantum statistics and thermodynamic cycles.

🌪️ Question 5: Pressure Profile Inside a Rotating Fluid Vortex

A cylindrical container of radius \( R \) and height \( H \) is completely filled with an incompressible, inviscid fluid of density \( \rho \). The container is rotated at a constant angular velocity \( \omega \) about its central vertical axis. After some time, the fluid reaches a steady state of rigid-body rotation.

A small hole is drilled at a height \( h < H \) at a radial distance \( r_0 \) from the axis. The pressure at this hole is measured using a manometer.

Tasks:

1. Derive the pressure as a function of radius \( r \), i.e., find \( P(r) \), inside the rotating fluid using Euler’s equation in cylindrical coordinates: \[ \rho \left( \frac{\partial \vec{v}}{\partial t} + (\vec{v} \cdot \nabla)\vec{v} \right) = -\nabla P + \rho \vec{g} \] Assume steady flow and purely azimuthal velocity \( \vec{v} = \omega r \hat{\theta} \).
2. Evaluate the pressure difference \( \Delta P = P(r_0) - P(0) \) at the same vertical height, and express it in terms of \( \rho \), \( \omega \), and \( r_0 \).
3. Compute the shape of the fluid surface. That is, find the height profile \( z(r) \) of the free surface due to the rotation.
4. A small neutrally buoyant particle is released near the axis. Discuss its motion in both the inertial and rotating frames. Estimate the radial acceleration experienced by the particle just after release.

Useful identity for total derivative in cylindrical polar coordinates (radial component only):

\[ (\vec{v} \cdot \nabla)v_r = \frac{v_\theta^2}{r} \]

Wow! To be very honest this is a very challenging problem that combines fluid dynamics, rotational motion, and pressure profiles. It requires a deep understanding of the physics involved and the ability to apply mathematical techniques to solve complex problems.

Topic-wise IPhO Practice Test Questions based on the Latest Syllabus (2025)

The syllabus of the International Physics Olympiad (IPhO) typically covers a wide range of topics in physics. Here is a general overview of the topics that are often included in the IPhO syllabus:

Mechanics

Download IPhO Mechanics Questions [PDF]

Topics:

• Kinematics
• Newton's Laws of Motion
• Conservation Laws (Momentum, Energy)
• Circular Motion
• Gravitation

Thermodynamics and Statistical Physics

Download IPhO Thermodynamics and Statistical Physics Questions [PDF]

Topics:

• Laws of Thermodynamics
• Kinetic Theory of Gases
• Heat Transfer
• Entropy and Probability
• Phase Transitions

Electromagnetism

Download IPhO Electromagnetism Questions [PDF]

Topics:

• Electric Fields and Forces
• Gauss's Law
• Electric Potential
• Capacitance and Dielectrics
• Magnetic Fields
• Ampere's Law
• Electromagnetic Induction
• AC Circuits

Optics and Waves

Download IPhO Optics and Waves Questions [PDF]

Topics:

• Geometrical Optics
• Wave Optics (Interference, Diffraction)
• Wave Properties (Superposition, Standing Waves)
• Doppler Effect
• Sound Waves

Modern Physics

• Special Theory of Relativity
• Photoelectric Effect
• Compton Effect
• Atomic Physics
• Nuclear Physics
• Elementary Particle Physics

Experiments and Laboratory Skills

• Measurement and Data Analysis
• Experimental Techniques
• Error Analysis

Mathematical Methods in Physics

• Calculus (Differential and Integral)
• Differential Equations
• Vector Analysis
• Linear Algebra
• Complex Numbers
• Fourier Analysis

Additional Topics

For the most up-to-date and detailed information on the IPhO syllabus for a specific year, it's advisable to refer to the official IPhO website.

IPhO 2025 Details

Name of the exam	International Physics Olympiad Practice Test (2025)
Type of Questions	Theoretical and practical questions
Exam Mode	IPhO is conducted in pen and paper format
Official IPhO Website	https://ipho.olimpicos.net/
Eligibility	Open to high school students who qualify through national-level competitions.
Language	English is the primary language for the exam, but translations may be available.
Topics Covered	Physics concepts from mechanics to modern physics.
Selection Process	Top performers in national exams are selected to represent their countries at the IPhO.
Competition Level	Extremely high; participants are some of the brightest physics students worldwide.
Awards	Gold, silver, and bronze medals for top performers; certificates for all participants.
Previous Host Countries	Varies each year; hosted in different countries around the world.
Preparation Materials	Various books, online resources, and sample papers are available for preparation.
Practice Online	IPhO Exam Online Preparation
Previous Year's Question Papers	IPhO Past Papers (1967 - 2025)

IPhO (1975 - 2025): Countries and Topics by Year

Year	Country	Problems (Topics)
2024	Iran	Greenhouse Effect, Trapping Ions and Cooling Atoms, Black Widow Pulsar, Heat Conduction in a Copper Rod, Diffraction from Phase Steps
2023	Japan	Soil Colloids, Neutron Stars, Water and Objects, Mass Measurement, Birefringence
2022	Switzerland	Permanent magnets, James Webb Space Telescope, Scaling laws, Planet, Cylindrical Diode
2021	Lithuania	Planetary Physics, Electrostatic Lens, Particles and Waves, Non-ideal Capacitors, LEDs
202O	IdPhO	Problem Mix, Anisotropic Friction, Laser Technologies, Crystallography
2019	Israel	Zero-length springs and slinky coils, The Physics of a Microwave Oven, Thermoacoustic Engine, Optical Measurements, Wiedemann-Franz Law
2018	Portugal	LIGO-GW150914, Where is the neutrino?, Physics of Live Systems, Paper Transistor, Viscoelasticity of a Polymer Thread
2017	Indonesia	Dark Matter, Earthquake, Volcano and Tsunami, Cosmic Inflation, Optics of a Salt Solution, Earthquake and Volcano Sensing
2016	Switzerland	Two Problems in Mechanics, Nonlinear Dynamics in Electric Circuits, Large Hadron Collider, Electrical Conductivity in 2D, Jumping Beads
2015	India	Particles from the Sun, The Extremum Principle, The Design of a Nuclear Reactor, Diffraction due to Helical Structure, Diffraction due to Surface Tension
2014	Kazakhstan	Three Problems, Van der Waals Gas, Gas Discharge, To see invisible!
2013	Denmark	The Maribo Meteorite, Plasmonic Steam Generator, The Greenlandic Ice Sheet, Speed of Light, Solar Cells
2012	Estonia	Focus on sketches, Kelvin water dropper, Protostar formation, The Magnetic Permeability of Water, Nonlinear Black Box
2011	Thailand	A Three-body Problem and LISA, An Electrified Soap Bubble, Scattering of an Ion by a Neutral Atom, Blackbox: Capacitive Displacement Sensor, Mechanical Blackbox: a cylinder with a ball inside
2010	Croatia	Image of a charge in a metallic object, Chimney physics, Simple model of an atomic nucleus, Elasticity of Sheets, Forces between Magnets
2009	Mexico	Evolution of the Earth-Moon System, Doppler Laser Cooling and Optical Molasses, Why are Stars so Large?, Wavelength of a Diode Laser, Birefringence of Mica
2008	Vietnam	Water-Powered Rice-Pounding Mortar, Cherenkov Light and Ring Imaging Counter, Change of Air Temperature in the Atmosphere, Differential Thermometric Method
2007	Iran	Black Holes, Air Bags, Binary Stars, Band Gap of Semiconductor Thin Films
2006	Singapore	Gravity in a Neutron Interferometer, Watching a Rod in Motion, Five Estimations, Interference, Reflection and Diffraction
2005	Spain	An ill Fated Satellite, Absolute Measurements of Electrical Quantities, Neutrons in a Gravitational Field, Planck's Constant in an Incandescent Lamp
2004	Korea	“Ping-Pong” Resistor, Rising Balloon, Atomic Probe Microscope, Mechanical "Black Box"
2003	Taiwan	A Swing with a Falling Weight, A Piezoelectric Crystal Resonator, Neutrino Mass and Neutron Decay, Optical Properties of Laser Diode
2002	Indonesia	Ground-Penetrating Radar, Sensing Electrical Signals, A Heavy Vehicle Moving on An Inclined Road, Physical Constants with Electrolysis, Optical Black Box
2001	Turkey	Four Problems, Binary Star System, Magnetohidrodynamic (MHD) Generator, Rotating Liquid
2000	United Kingdom	Five Problems, Cathode Ray Tube, Gravitational Waves and Light, CDROM Spectrometer, The Magnetic Puck
1999	Italy	Absorption of Radiation by a Gas, Magnetic field with a V-shaped wire, A Space Probe to Jupiter, Torsion pendulum
1998	Iceland	Rolling of a Hexagonal Prism, Water under an Ice Cap, Faster than Light?, Electromagnetism
1997	Canada	Scalings, Nuclear Masses and Stability, Solar-Powered Aircraft, Characterization of the Bimorph
1996	Norway	Five Problems, Dynamics of Electrons and Cylinders, Moon and Tides, Gravity and Magnetism
1995	Australia	Gravitational Red Shift and Stellar Mass, Sound Propagation, Cylindrical Buoy, Terminal Velocity in a Viscous Liquid, Difiraction and Scattering of Laser Light
1994	China	Relativistic Particle, Superconducting Magnet, Collision of Discs with Surface Friction, Light Reflectivity of a Transparent Dielectric, Two Terminal Black Box
1993	USA	Atmospheric Electricity, Laser Forces on a Transparent Prism, Electron Beam, Heat of Vaporization of Nitrogen, Magnetic Moments and Fields
1992	Finland	A Rotating Satellite, The Longitudinal Motion of a Linear Molecule, A Satellite in Sunshine, Electric Breakdown of Air, A Grating and Optical Filters
1991	Cuba	Friction on Impact, Relativistic Square, Cooling Atoms by Laser, Three Terminal Black Box
1990	Netherlands	X-ray Diffraction from a Crystal, Electric Experiments in the Magnetosphere, The Rotating Neutron Star, LED Efficiency, Two Magnets
1989	Poland	Boiling Liquids, Rotating Masses, Proton Microscope, Piezoelectric Discs
1988	Austria	Spectroscopy of Particle Velocities, Maxwell's Wheel, Recombination of Ions in Ionized Gas, Polarized Light, Electron Tube
1987	East Germany	Ascending Moist Air, Electrons in a Magnetic Field, Infinite LC-grid, Refractive Indices
1986	United Kingdom	Wave Interference, Seismic Waves, Masses and Springs, Pendant Drop, Microcomputer
1985	Yugoslavia	Antenna Array, Hall Effect, Escaping the Solar System, Brass Disk, Permanent Magnets
1984	Sweden	Mirage, Seiching, Electrical Filter, Diode, Capacitor and Resistor, Glow Discharge Lamp
1983	Romania	Jumping Particle, Different kind of Oscillation, Prisms, Compton Scattering, IPhO's LOGO
1982	West Germany	Fluorescent lamp, Oscillating coat hanger, Hot-air-balloon, Lens Experiment, Motion of a Rolling Cylinder
1981	Bulgaria	Gas Container Rocket, Electric Lamp, Detecting Astronomical Radiowaves, Elastic Rubber Cord
1979	Soviet Union	To the Moon!, Influence of Humidity on Scales, Reflectors on the Moon, Black Box
1977	Czechoslovakia	Otto Cycle, Rectangular Soap Film, Electron Gun
1976	Hungary	Spinning Block Inside a Sphere, A Valve in a Cylinder, Air Bubble inside a Glass Sphere, Thermal Properties of the X material
1975	East Germany	Rotating Rod, Thick Lens, Ions in a Magnetic Field, Semiconductor Element
1974	Poland	Hydrogen Atoms Colliding, Bending Light, Surviving with Thermodynamics, Diodes in a Black Box
1972	Romania	Three Cylinders, Molecular Physics, Dielectric Liquid, Geometrical Optics and Interference, Two Cylinders
1971	Bulgaria	Connected Masses on a Prism, Mercury Barometer, Batteries, Capacitors and Resistors in a Cube, Spherical Aquarium, Rheostat Dissipation
1970	Soviet Union	Carrying a Bar, A Chemistry Problem (Salt Crystals), Spherical Capacitors, A Telescope with a Spherical Mirror, Three Lenses
1969	Czechoslovakia	Three Carts, Water inside a Copper Calorimeter, Suspended Charged Ball, Glass Plate above a Glass Cube
1968	Hungary	Block and Cylinder on an Inclined Plane, Mixing Toluene, Glass Semi-cylinder, Three Black Boxes
1967	Poland	Shooting a Ball, Infinite Network of Resistors, Heating Balls, Heating a Vessel, Heating Petroleum

Important Topics in IPhO with Percentage Distribution of Questions

Based on questions from IPhO (1967 to 2025), the following table summarizes some of the most important topics with their respective percentage distribution of questions. This data is useful for students preparing for the IPhO exam, as it highlights the most important topics to focus on.

Topic	Percentage	Subtopics
Mechanics	30%	Kinematics, Dynamics, Statics
Optics	25%	Geometrical Optics, Wave Optics, Quantum Optics
Electromagnetism	20%	Electromagnetic Waves, Electromagnetic Fields, Electromagnetic Induction
Thermodynamics	15%	Thermal Properties of the X material, Thermal Properties of the Y material, Thermal Properties of the Z material
Nuclear Physics	10%	Nuclear Reactions, Nuclear Decay, Nuclear Fusion
Fluid Dynamics	5%	Fluid Statics, Fluid Kinematics, Fluid Dynamics
Acoustics	5%	Sound Waves, Sound Propagation, Sound Interference
Relativity	5%	Special Relativity, General Relativity, Gravitational Waves
Astronomy	5%	Astronomical Measurements, Celestial Mechanics, Stellar Evolution

Note: The percentages are approximate and may vary slightly from year to year.

Source: Analysis of 58 Years of IPhO Questions from the IPhO Official Website

Guide Books for IPhO 2025

Category	Book/Resource	Description
Mechanics	Introduction to Mechanics by David Morin	Provides a strong foundation in classical mechanics, including topics like Lagrangian mechanics useful for advanced problem-solving.
	Physics by Halliday, Resnick, and Krane/Walker	A comprehensive textbook covering all areas of physics.
Electromagnetism	Introduction to Electrodynamics by David Griffiths	A well-regarded textbook covering fundamentals of electromagnetism.
	Electricity and Magnetism by Purcell and Morin	Focuses on electromagnetism with an emphasis on multidimensional and vector calculus approaches.
Optics	Optics by Hecht	A comprehensive and detailed resource on optics, covering IPhO-relevant topics.
Problem-Solving	Problems in General Physics by I.E. Irodov	Offers a wide range of challenging problems to improve problem-solving skills.
	Problems in Classical Physics by A.S. Vinogradov	Covers various physics topics and is excellent for rigorous practice.
Additional Resources	Past IPhO Problems	Includes previous year's solved problems.
	National Physics Olympiad (NSEP/IOQP) Materials	Practicing national olympiad problems is also beneficial for preparation.

What is the International Physics Olympiad (IPhO)?

The International Physics Olympiad (IPhO) is a prestigious annual competition that brings together talented high school students from around the world to test their knowledge and problem-solving skills in physics. This international event serves as a platform for young physics enthusiasts to showcase their abilities on a global stage.

Impact and Recognition

Participating in the IPhO not only provides recognition and prestige but also helps nurture a deep passion for physics among young talents. It serves as a stepping stone for future careers in physics and related fields, contributing to the advancement of science and technology on a global scale.

The International Physics Olympiad (IPhO) is a highly competitive and respected event that brings together exceptional young physicists from around the world to showcase their knowledge and skills in physics. It offers a unique opportunity for global collaboration, academic recognition, and personal growth in the field of physics.

What is IPhO Mock Test?

IPhO Mock Tests are model tests for the online practice of the International Physics Olympiad Exam. This help students create a better exam preparation strategy. If you treat IPhO mock tests as actual tests, you will perform well in the online IPhO exam as well. So instead of just rote learning concepts, practice IPhO mock tests to measure your strengths and weakness. IPhO mocks will help you in developing an effective study strategy.

Benefits/Advantages of Practicing Online IPhO Mock Tests Series (2025)

The practice of online mock tests is important for candidates appearing in the upcoming International Physics Olympiad Exam as it is similar to the real exam and helps students assess their preparation.

By practicing free online IPhO mock tests, you get a fair idea about the real test pattern and reduce pre-exam anxiety. IPhO mock tests are important because of the time-bound practice they provide. Multiple attempts of the IPhO mock test will help you revise the entire syllabus. IPhO mock tests help you remember basic concepts and perform better in the actual exams. IPhO Mock tests provide the scope of the question paper. IPhO Mock tests improve your time management skill.

Attempting multiple mock tests help students revise the entire IPhO exam syllabus. This way they memorize concepts and perform well in the IPhO exam. Mock tests make students familiar with the style and scope of the IPhO question paper.