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Key Facts: PAU Physics (Castilla y León) Exam

90 min

Time Limit

Comisión Organizadora CyL

0–10

Grading Scale

Junta de Castilla y León

4.0

Min. Access Phase Mark

PAU Regulations

EUR 76.82

Base Exam Fee

Junta de Castilla y León 2026

100

Practice Questions

English Study Adaptation

The Castilla y León PAU Physics (Física) exam is a 90-minute examination set by the Comisión Organizadora de Castilla y León (USAL, UVa, UBU, ULE) with a registration fee of EUR 76.82 (Access Phase base fee). Grades are awarded on a 0–10 scale, with a minimum 4.0 required to average with high school GPA. This study portal provides an English-language MCQ study adaptation featuring 100 practice questions with real calculations covering all 5 official curriculum modules.

Sample PAU Physics (Castilla y León) Practice Questions

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

1Two point masses m1 = 600 kg and m2 = 1200 kg are separated by a distance r = 3.0 m in a vacuum. Using Newton's Law of Universal Gravitation (G = 6.67 x 10^-11 N m^2/kg^2), what is the magnitude of the gravitational attraction between them?
A.5.34 x 10^-6 N
B.1.60 x 10^-5 N
C.2.67 x 10^-6 N
D.4.80 x 10^-5 N
Explanation: Applying Newton's Law of Universal Gravitation F = G * m1 * m2 / r^2: F = (6.67 x 10^-11) * 600 * 1200 / (3.0)^2 = (6.67 x 10^-11) * 720,000 / 9 = (6.67 x 10^-11) * 80,000 = 5.336 x 10^-6 N, which rounds to 5.34 x 10^-6 N.
2If the acceleration due to gravity at Earth's surface is g0 = 9.80 m/s^2, what is the magnitude of the gravitational field intensity g at an altitude h = 2 R_E above Earth's surface (where R_E is Earth's radius)?
A.3.27 m/s^2
B.1.09 m/s^2
C.2.45 m/s^2
D.4.90 m/s^2
Explanation: The distance from Earth's center is r = R_E + h = R_E + 2 R_E = 3 R_E. The gravitational field follows an inverse-square law: g(r) = G * M_E / r^2 = G * M_E / (3 R_E)^2 = g0 / 9. Therefore, g = 9.80 / 9 = 1.09 m/s^2.
3What is the gravitational potential V at a point located at distance r = 3 R_E from Earth's center? (Use Earth mass M_E = 5.97 x 10^24 kg, R_E = 6.37 x 10^6 m, G = 6.67 x 10^-11 N m^2/kg^2).
A.-6.25 x 10^7 J/kg
B.-3.13 x 10^7 J/kg
C.-2.08 x 10^7 J/kg
D.-1.04 x 10^7 J/kg
Explanation: Gravitational potential is given by V = -G * M_E / r. Substituting r = 3 R_E = 3 * 6.37 x 10^6 m = 1.911 x 10^7 m gives V = -(6.67 x 10^-11 * 5.97 x 10^24) / (1.911 x 10^7) = -3.982 x 10^14 / 1.911 x 10^7 = -2.08 x 10^7 J/kg.
4Calculate the work done by the gravitational force when moving a mass m = 200 kg from Earth's surface (r1 = R_E) to a distance r2 = 2 R_E from Earth's center.
A.-6.25 x 10^9 J
B.+6.25 x 10^9 J
C.-1.25 x 10^10 J
D.+3.13 x 10^9 J
Explanation: The work done by gravity is W_grav = -ΔU = -m * (V2 - V1) = G * M_E * m * (1/r2 - 1/r1). Here, 1/(2 R_E) - 1/R_E = -1/(2 R_E). Thus W_grav = -(G * M_E * m) / (2 R_E) = -(6.67 x 10^-11 * 5.97 x 10^24 * 200) / (2 * 6.37 x 10^6) = -6.25 x 10^9 J. The negative sign indicates gravity opposes outward displacement.
5A satellite orbits Earth in a circular path at an altitude h = 1000 km above the surface. What is its orbital speed? (M_E = 5.97 x 10^24 kg, R_E = 6370 km, G = 6.67 x 10^-11 N m^2/kg^2).
A.7.91 km/s
B.6.45 km/s
C.8.24 km/s
D.7.35 km/s
Explanation: Orbital radius r = R_E + h = 6370 km + 1000 km = 7370 km = 7.37 x 10^6 m. Equating gravitational force to centripetal force yields v = sqrt(G * M_E / r) = sqrt((6.67 x 10^-11 * 5.97 x 10^24) / (7.37 x 10^6)) = sqrt(5.403 x 10^7) = 7350 m/s = 7.35 km/s.
6What is the orbital period T of a satellite in a circular orbit around Earth at radius r = 4 R_E? (M_E = 5.97 x 10^24 kg, R_E = 6.37 x 10^6 m, G = 6.67 x 10^-11 N m^2/kg^2).
A.5.63 hours
B.11.25 hours
C.1.41 hours
D.24.0 hours
Explanation: Orbital radius r = 4 * 6.37 x 10^6 m = 2.548 x 10^7 m. Using Kepler's Third Law T = 2 * pi * sqrt(r^3 / (G * M_E)) = 2 * pi * sqrt((2.548 x 10^7)^3 / (3.982 x 10^14)) = 2 * pi * sqrt(1.655 x 10^22 / 3.982 x 10^14) = 2 * pi * sqrt(4.156 x 10^7) = 2 * pi * 6447 s = 40500 s = 11.25 hours.
7Determine the escape velocity from the surface of the Moon. (Moon mass M_M = 7.35 x 10^22 kg, Moon radius R_M = 1.74 x 10^6 m, G = 6.67 x 10^-11 N m^2/kg^2).
A.2.37 km/s
B.1.68 km/s
C.4.74 km/s
D.11.2 km/s
Explanation: Escape velocity is given by v_esc = sqrt(2 * G * M_M / R_M) = sqrt(2 * 6.67 x 10^-11 * 7.35 x 10^22 / (1.74 x 10^6)) = sqrt(9.805 x 10^12 / 1.74 x 10^6) = sqrt(5.635 x 10^6) = 2374 m/s = 2.37 km/s.
8What is the total mechanical energy E of a 400 kg satellite in a circular orbit around Earth at radius r = 2 R_E? (M_E = 5.97 x 10^24 kg, R_E = 6.37 x 10^6 m, G = 6.67 x 10^-11 N m^2/kg^2).
A.-1.25 x 10^10 J
B.+6.25 x 10^9 J
C.-6.25 x 10^9 J
D.-3.13 x 10^9 J
Explanation: For a circular orbit, total mechanical energy is E = U / 2 = -G * M_E * m / (2 r). With r = 2 R_E, E = -G * M_E * m / (4 R_E) = -(6.67 x 10^-11 * 5.97 x 10^24 * 400) / (4 * 6.37 x 10^6) = -1.593 x 10^17 / 2.548 x 10^7 = -6.25 x 10^9 J.
9According to Kepler's Third Law, the ratio T^2 / r^3 for planets orbiting the Sun depends ONLY on which of the following quantities?
A.The mass of the Sun
B.The mass of the orbiting planet
C.The orbital eccentricity
D.The rotational speed of the planet
Explanation: Kepler's Third Law states T^2 / r^3 = 4 * pi^2 / (G * M_Sun). The constant of proportionality depends exclusively on the universal gravitational constant G and the mass of the central body (the Sun), being independent of the planet's mass.
10A geostationary satellite orbits Earth with a period T = 24 hours in a circular equatorial orbit of radius r ≈ 42,200 km. What is its altitude h above Earth's surface? (Earth radius R_E = 6,370 km).
A.42,200 km
B.21,100 km
C.48,570 km
D.35,830 km
Explanation: Altitude h is the distance from Earth's surface to the satellite: h = r - R_E = 42,200 km - 6,370 km = 35,830 km (often rounded to ~35,800 km).

About the PAU Physics (Castilla y León) Exam

The Castilla y León PAU Physics (Física) exam is the official standardized university entrance examination for 2nd Bachillerato students in Castilla y León, Spain. Note: The questions provided in this practice bank are an English-language multiple-choice study adaptation designed to help students master core physical principles, calculations, and concepts for the Castilla y León PAU 2026 Physics curriculum (Física 2º Bachillerato). The exam evaluates competence across gravitational fields, electrostatics, magnetostatics, electromagnetic induction, wave mechanics, geometrical and physical optics, special relativity, photoelectric effect, and nuclear physics.

Exam sponsor: Comisión Organizadora de la PAU de Castilla y León (USAL, UVa, UBU, ULE / Junta de Castilla y León). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written examination consisting of mandatory theoretical/conceptual questions and optional problem-solving blocks (adapted here into 100 multiple-choice practice questions).

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 76.82 base registration fee for PAU Access Phase (plus EUR 10.33 per voluntary subject) set by Junta de Castilla y León.

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

Gravitational force, field intensity vector, gravitational potential energy, conservative fields, satellite speed, orbital period, escape velocity, and Kepler's third law.

20%

Electric Field

Coulomb's law, electric field intensity, electrostatic potential, electric potential energy, Gauss's law, work done by electric force, and charged particle motion in electric fields.

20%

Magnetic Field and Electromagnetic Induction

Magnetic force on moving charges (Lorentz force) and current conductors, Biot-Savart law, parallel currents, magnetic flux, Faraday-Lenz law of induction, and induced electromotive force.

20%

Wave Motion and Geometrical & Physical Optics

Harmonic wave parameters (amplitude, wavelength, frequency, wave number), wave energy, sound intensity levels in decibels, Snell's law of refraction, total internal reflection, thin lens equations, image formation, and eye defects.

20%

Special Relativity, Quantum & Nuclear Physics

Postulates of special relativity, time dilation, relativistic energy, photon energy, work function, photoelectric threshold, de Broglie wavelength, mass defect, binding energy per nucleon, and radioactive decay kinetics.

Preparing for the PAU Physics (Castilla y León) 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: Written examination consisting of mandatory theoretical/conceptual questions and optional problem-solving blocks (adapted here into 100 multiple-choice practice questions).
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 76.82 base registration fee for PAU Access Phase (plus EUR 10.33 per voluntary subject) set by Junta de Castilla y León. 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

PAU Physics (Castilla y León): Suggested Study Strategy

1Master vector notation and signs for gravitational and electric fields, ensuring you correctly determine field direction and potential scalar values.
2Memorize key physical constants ($G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$, $c = 3 \times 10^8 \text{ m/s}$, $e = 1.6 \times 10^{-19} \text{ C}$, $h = 6.63 \times 10^{-34} \text{ J s}$).
3Practice multi-step orbital calculations including escape velocity, satellite speed, energy conservation, and Kepler's third law ($T^2/r^3$).
4Understand the direction of induced current using Lenz's law ('nature opposes change in flux') and apply Faraday's law (\mathcal{E} = -d\Phi/dt).
5Become proficient in Snell's law ($n_1 \sin\theta_1 = n_2 \sin\theta_2$) and calculating critical angles for total internal reflection (\sin\theta_c = n_2/n_1).
6For optics, strictly follow sign conventions for focal length and distances when using the thin lens equation ($1/f' = 1/s' - 1/s$).
7Master photoelectric effect equations: $E_{photon} = hf = W_0 + E_{k,max}$, and understand stopping potential ($E_{k,max} = e V_s$).
8Calculate mass defect \Delta m = [Z m_p + (A-Z) m_n] - m_{nucleus} and binding energy $E_b = \Delta m \cdot c^2$ accurately, converting between atomic mass units (u) and MeV.

Frequently Asked Questions

What is the format of the Castilla y León PAU Physics exam?

The official Castilla y León PAU Physics exam is a 90-minute written examination consisting of problem-solving exercises and theoretical conceptual questions in Spanish. The question bank on this website is an English-language multiple-choice study adaptation designed to build calculation fluency and conceptual mastery for the official curriculum.

Who sets the PAU Physics exam in Castilla y León?

The exam is coordinated by the Comisión Organizadora de la Prueba de Acceso a la Universidad de Castilla y León, which comprises representatives from the regional government (Junta de Castilla y León) and the four public universities: USAL, UVa, UBU, and ULE.

How is the PAU Physics score calculated?

The exam is graded on a scale from 0 to 10 points. In the Access Phase (Fase de Acceso), a minimum mark of 4.0 out of 10 is required. The overall admission mark combines 60% Bachillerato GPA and 40% PAU Access Phase mark (must be >= 5.0). In the Voluntary Phase (Fase de Admisión), students can gain up to 4 additional points depending on university degree weighting parameters (typically 0.2 per subject).

What calculators are allowed in the Castilla y León PAU Physics exam?

Students may use scientific, non-programmable calculators that do not have graphic display capabilities, text storage, symbolic algebra systems (CAS), or networking functions, in accordance with the official rules published by the examination commission.

Are these practice questions identical to the official exam?

These 100 questions are an English-language MCQ study adaptation based on the official 2026 2nd Bachillerato Physics curriculum in Castilla y León. While the official exam features open-ended written problems in Spanish, these questions mirror the mathematical and physical concepts, constants, and problem types required for success.