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Key Facts: Madrid PAU Physics Exam

PAU Organising Commission / UCM

Exam Body

Community of Madrid University Admissions

90 min

Duration

Madrid PAU Regulations

0–10

Scoring

PAU Spain Marking Scheme

2º Bach.

Target Level

Madrid Education Department

€93.02

Registration Fee

UCM PAU Fee Schedule

Sample Madrid PAU Physics Practice Questions

Try these sample questions to review concepts for the Madrid PAU Physics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1According to Newton's law of universal gravitation, how does the gravitational force between two point masses change if the distance between their centers is tripled?
A.It decreases to 1/9 of its original value.
B.It decreases to 1/3 of its original value.
C.It increases by a factor of 9.
D.It decreases to 1/6 of its original value.
Explanation: Newton's law of universal gravitation states F = G*(m1*m2)/r^2. When separation distance r is multiplied by 3, the force becomes F' = G*(m1*m2)/(3r)^2 = (1/9)*F. Thus, force decreases to 1/9 of its original value.
2At an altitude above Earth's surface equal to Earth's radius (h = R_E), what is the magnitude of the gravitational acceleration g? (Assume surface acceleration g_0 = 9.80 m/s²).
A.2.45 m/s²
B.4.90 m/s²
C.9.80 m/s²
D.1.23 m/s²
Explanation: Gravitational acceleration at radial distance r from Earth's center is g = G*M_E / r^2. At Earth's surface r = R_E, g_0 = 9.80 m/s². At altitude h = R_E, total radial distance is r = R_E + R_E = 2 R_E. Thus g = G*M_E / (2 R_E)^2 = g_0 / 4 = 9.80 / 4 = 2.45 m/s².
3A satellite orbits Earth in a circular path at an altitude equal to Earth's radius (h = R_E = 6.37 × 10⁶ m). Given Earth's mass M_E = 5.97 × 10²⁴ kg and G = 6.674 × 10⁻¹¹ N m²/kg², what is the orbital speed of the satellite?
A.5.59 × 10³ m/s
B.7.91 × 10³ m/s
C.3.95 × 10³ m/s
D.1.12 × 10⁴ m/s
Explanation: For a circular orbit, gravitational attraction provides centripetal force: G*M_E*m / r^2 = m*v^2 / r, leading to v = sqrt(G*M_E / r). The orbital radius is r = R_E + h = 2 R_E = 1.274 × 10⁷ m. Evaluating v = sqrt((6.674 × 10⁻¹¹ × 5.97 × 10²⁴) / 1.274 × 10⁷) = sqrt(3.127 × 10⁷) = 5.59 × 10³ m/s.
4Two planets orbit a central star in circular orbits. Planet A has orbital radius R, and Planet B has orbital radius 4R. If Planet A's orbital period is T_A = 2.0 years, what is Planet B's orbital period T_B?
A.16.0 years
B.8.0 years
C.32.0 years
D.4.0 years
Explanation: By Kepler's Third Law, T^2 / r^3 is constant for orbits around the same mass. Thus (T_B / T_A)^2 = (r_B / r_A)^3 = (4R / R)^3 = 64. Taking the square root gives T_B / T_A = 8, so T_B = 8 × 2.0 = 16.0 years.
5What is the escape velocity from the surface of a planet that has twice the mass of Earth (M_P = 2 M_E) and half the radius of Earth (R_P = 0.5 R_E)? (Earth's escape velocity v_e,Earth = 11.2 km/s).
A.22.4 km/s
B.11.2 km/s
C.44.8 km/s
D.15.8 km/s
Explanation: Escape velocity is v_e = sqrt(2 G M / R). For the new planet: v_e,P = sqrt(2 G (2 M_E) / (0.5 R_E)) = sqrt(4 * (2 G M_E / R_E)) = 2 * v_e,Earth = 2 * 11.2 km/s = 22.4 km/s.
6How is the kinetic energy E_k of a satellite in a circular orbit related to its gravitational potential energy E_p (with standard infinity reference)?
A.E_k = -1/2 * E_p
B.E_k = E_p
C.E_k = -E_p
D.E_k = -2 * E_p
Explanation: For circular orbit, centripetal force yields E_k = 1/2 m v^2 = G M m / (2 r). Gravitational potential energy is E_p = -G M m / r. Comparing expressions shows E_k = -1/2 * E_p.
7A satellite of mass m = 500 kg is transferred from a circular orbit of radius r_1 = 2 R_E to a higher circular orbit of radius r_2 = 4 R_E. Given G*M_E = 3.986 × 10¹⁴ m³/s² and R_E = 6.37 × 10⁶ m, what is the work required by the engines?
A.3.91 × 10⁹ J
B.7.82 × 10⁹ J
C.1.56 × 10¹⁰ J
D.1.95 × 10⁹ J
Explanation: Total mechanical energy in circular orbit is E = -G M_E m / (2 r). Work required is W = Delta E = E_2 - E_1 = (G M_E m / 2) * (1/r_1 - 1/r_2). Substituting values: W = (3.986 × 10¹⁴ × 500 / 2) * (1/(1.274 × 10⁷) - 1/(2.548 × 10⁷)) = 9.965 × 10¹⁶ * 3.925 × 10⁻⁸ = 3.91 × 10⁹ J.
8Which of the following statements correctly describes a geostationary satellite orbit around Earth?
A.Its orbital plane must coincide with Earth's equatorial plane, moving west to east with a period of 24 hours.
B.Its orbit can pass directly over Earth's geographic North and South poles with a period of 12 hours.
C.Its orbital speed is equal to Earth's surface escape velocity.
D.It experiences zero net gravitational force from Earth.
Explanation: A geostationary satellite remains stationary relative to a point on Earth's surface. This requires a circular equatorial orbit, rotating west to east with an orbital period matching Earth's rotation period (~24 hours).
9Calculate the altitude h above Earth's surface for a geostationary satellite. (Earth mass M_E = 5.97 × 10²⁴ kg, G = 6.674 × 10⁻¹¹ N m²/kg², Earth radius R_E = 6.37 × 10⁶ m, period T = 86,400 s).
A.3.58 × 10⁷ m (35,800 km)
B.4.22 × 10⁷ m (42,200 km)
C.6.37 × 10⁶ m (6,370 km)
D.1.28 × 10⁷ m (12,800 km)
Explanation: From Kepler's 3rd Law T^2 = 4 pi^2 r^3 / (G M_E), orbital radius is r = (G M_E T^2 / (4 pi^2))^(1/3) = 4.22 × 10⁷ m. Altitude above Earth's surface is h = r - R_E = 4.22 × 10⁷ - 6.37 × 10⁶ = 3.58 × 10⁷ m = 35,800 km.
10What is the gravitational potential V at a point on Earth's surface? (Earth mass M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.674 × 10⁻¹¹ N m²/kg²).
A.-6.25 × 10⁷ J/kg
B.-9.80 J/kg
C.+6.25 × 10⁷ J/kg
D.-3.98 × 10¹⁴ J/kg
Explanation: Gravitational potential is V = -G M_E / R_E. Substituting values: V = -(6.674 × 10⁻¹¹ × 5.97 × 10²⁴) / 6.37 × 10⁶ = -6.25 × 10⁷ J/kg.

About the Madrid PAU Physics Exam

Comprehensive practice exam bank for Madrid PAU Physics (Física). Features 100 high-quality practice questions in English, covering topics from the 2nd Bachillerato Physics curriculum and Community of Madrid PAU university entrance examination standards, covering gravitation, electromagnetism, waves, optics, and modern physics.

Exam sponsor: PAU Organising Commission of the Community of Madrid / Universidad Complutense de Madrid (UCM). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Question count not published by the exam provider

Time Limit

90 minutes (1.5 hours)

Passing Score

Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).

Exam / Certification Fees

EUR 93.02 base registration fee for compulsory Access Phase in Community of Madrid (or ~11.63 € per optional subject in voluntary phase).

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

20%

Gravitational Field & Celestial Mechanics

Newton's law of universal gravitation, gravitational field strength and potential, orbital dynamics, Kepler's laws, escape velocity, and satellite energy.

25%

Electromagnetic Field & Induction

Coulomb's law, electric field and potential, motion of charges in E and B fields, magnetic force on currents, Ampère's law, Faraday-Lenz induction, and motional emf.

25%

Waves, Harmonic Motion & Acoustics

Simple harmonic motion, wave parameters, wave equation, sound intensity and decibels, Doppler effect, interference, diffraction, and standing waves.

15%

Geometrical & Physical Optics

Snell's law of refraction, total internal reflection, thin lenses and spherical mirrors, optical instruments, wave optics, interference, and Brewster polarization.

15%

Modern Physics, Quantum & Relativity

Photoelectric effect, photon energy, de Broglie wavelength, atomic energy levels, mass defect and nuclear binding energy, radioactivity, and special relativity.

Preparing for the Madrid PAU Physics Exam

What You Need to Know

  • Passing score: Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass).
  • Assessment: Question count not published by the exam provider
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 93.02 base registration fee for compulsory Access Phase in Community of Madrid (or ~11.63 € per optional subject in voluntary phase). Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Frequently Asked Questions

What is the format of the Madrid PAU Physics exam?

The official Madrid PAU Physics exam is a 90-minute written assessment consisting of theoretical conceptual questions and quantitative calculation problems across two optional blocks (Option A / Option B or structured problem sets). This OpenExamPrep question bank adapts these competencies into 100 rigorous multiple-choice items.

What tools or calculators are permitted during the PAU Physics exam in Madrid?

Non-programmable, non-graphing scientific calculators without alphanumeric storage capability are permitted. Fundamental physical constants are provided on the official exam cover sheet.

How long is the PAU Physics exam in Madrid?

Students are allotted 90 minutes (1.5 hours) to complete the examination.

How is the Physics mark weighted for university admission in Madrid?

Physics is a key subject for Engineering, Architecture, Physics, Mathematics, and STEM degrees in Madrid universities, carrying a maximum weight of 0.2 in the voluntary phase of PAU, adding up to 2 extra points to the admission mark.

What passing score is required on the PAU Physics exam?

The exam is scored from 0 to 10. In the compulsory Access Phase, a minimum grade of 4.0 is required to average with the Bachillerato GPA. In the voluntary phase, a minimum mark of 5.0 is required for the score to be weighted.