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2026 Statistics
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 test your PAU Physics (Castilla y León) exam readiness. 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) Practice Questions
Verified exam format metadata for Castilla y León PAU Physics Exam / Física 2º Bachillerato is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.