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Madrid PAU General Sciences - independent foundations study materials
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Madrid PAU General Sciences - independent foundations practice questions

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Question 1Scientific questions, evidence and quantitative reasoning

In a controlled scientific experiment, what is the difference between an independent variable and a dependent variable?

  1. The independent variable is intentionally manipulated by the experimenter; the dependent variable is measured as the outcome response. Correct answer.
  2. The independent variable is kept constant throughout; the dependent variable is changed at random.
  3. The dependent variable is manipulated; the independent variable remains unmeasured.
  4. Both variables are held constant to serve as negative controls.

Explanation

In scientific testing, the researcher alters the independent variable (cause) and observes changes in the dependent variable (effect) while holding confounding variables constant.

Question 2Scientific questions, evidence and quantitative reasoning

Which energy source is classified as non-renewable due to its finite geological replenishment timescale?

  1. Geothermal energy
  2. Natural gas Correct answer.
  3. Wind power
  4. Solar photovoltaics

Explanation

Natural gas is a fossil fuel formed over millions of years from organic remains under high pressure. Its depletion rate vastly exceeds its natural formation rate.

Question 3Scientific questions, evidence and quantitative reasoning

How does achieving high vaccination coverage in a population establish 'herd immunity'?

  1. It mutates pathogens into harmless strains.
  2. It eliminates the need for personal hygiene.
  3. It reduces the proportion of susceptible individuals, preventing disease transmission to unvaccinated individuals. Correct answer.
  4. It provides lifelong genetic immunity passed to unborn children.

Explanation

When a high percentage of a population is immune to an infectious agent, the chain of transmission is broken, indirectly protecting vulnerable or unvaccinated individuals.

Question 4Scientific questions, evidence and quantitative reasoning

What specialized molecular tools are used in recombinant DNA technology to cleave DNA molecules at specific palindromic nucleotide sequences?

  1. DNA ligases
  2. RNA polymerases
  3. Reverse transcriptases
  4. Restriction endonucleases Correct answer.

Explanation

Restriction endonucleases ('molecular scissors') recognize specific palindromic DNA sequences (e.g., GAATTC for EcoRI) and cut the sugar-phosphate backbone.

Question 5Scientific questions, evidence and quantitative reasoning

What is the primary function of a 'control group' in a clinical drug trial?

  1. To provide a baseline for comparison to ensure observed therapeutic effects are caused by the active drug rather than placebo effects or natural recovery Correct answer.
  2. To guarantee that all trial participants receive active medication
  3. To increase the trial cost
  4. To test higher doses of the drug

Explanation

A control group receives a placebo or standard treatment under identical conditions. Comparing outcomes isolates the true pharmacological efficacy of the new drug.

Question 6Scientific questions, evidence and quantitative reasoning

Which physical property distinguishes thermoplastic polymers (e.g., polyethylene) from thermosetting polymers (e.g., bakelite)?

  1. Thermoplastics decompose without melting when heated.
  2. Thermoplastics soften and melt upon heating, allowing them to be repeatedly reshaped and recycled. Correct answer.
  3. Thermosets can be melted and remolded indefinitely.
  4. Thermoplastics possess permanent covalent cross-links between polymer chains.

Explanation

Thermoplastics consist of linear or branched chains held together by weak intermolecular forces. Heating breaks these forces, allowing the polymer to melt and be recycled. Thermosets contain rigid covalent cross-links that degrade rather than melt upon heating.

Question 7Scientific questions, evidence and quantitative reasoning

In the CRISPR-Cas9 genome editing system, what component directs the Cas9 endonuclease to the precise target genomic DNA site?

  1. A synthetic transfer RNA molecule
  2. A restriction enzyme fragment
  3. A single guide RNA (sgRNA) sequence complementary to the target DNA strand Correct answer.
  4. A phospholipid vesicle

Explanation

The CRISPR-Cas9 system uses a single guide RNA (sgRNA) containing a 20-nucleotide sequence complementary to the target genomic region, directing Cas9 to generate a precise double-strand break.

Question 8Scientific questions, evidence and quantitative reasoning

What is the main purpose of conducting a Life Cycle Assessment (LCA) for a commercial product?

  1. To maximize retail market pricing
  2. To measure corporate financial tax liabilities
  3. To speed up assembly line manufacturing
  4. To evaluate environmental impacts across all stages from raw material extraction to final disposal ('cradle-to-grave') Correct answer.

Explanation

A Life Cycle Assessment (LCA) quantifies energy inputs, raw material consumption, and environmental emissions across all lifecycle stages: raw extraction, processing, distribution, use, and end-of-life disposal or recycling.

Question 9Scientific questions, evidence and quantitative reasoning

How does a pumped-storage hydroelectric energy plant balance electrical grid stability during peak demand periods?

  1. It pumps water uphill into a reservoir using excess low-cost electricity, then releases water downhill through turbines during high electricity demand. Correct answer.
  2. It burns natural gas to heat reservoir water for steam turbines.
  3. It uses solar panels to boil reservoir water.
  4. It operates continuous nuclear fission in deep reservoir water.

Explanation

Pumped-storage hydro acts as a large-scale energy storage system. During low-demand periods, excess grid electricity pumps water into an elevated reservoir. During peak demand, released water drives hydroelectric turbines to generate electricity rapidly.

Question 10Scientific questions, evidence and quantitative reasoning

Which unique property of engineered nanomaterials (particles sized 1-100 nm) enhances their chemical reactivity compared to bulk materials?

  1. Decreased magnetic field interaction
  2. Significantly higher surface area-to-volume ratio Correct answer.
  3. Reduced gravitational pull
  4. Complete loss of electrical conductivity

Explanation

As particle size decreases to the nanoscale, the proportion of atoms exposed on the surface increases dramatically. This high surface area-to-volume ratio increases chemical reactivity and catalytic efficiency.

Question 11Scientific questions, evidence and quantitative reasoning

How can bacterial populations rapidly spread antibiotic resistance genes via horizontal gene transfer?

  1. By undergoing meiotic gamete fusion
  2. By deactivating bacterial cell walls completely
  3. Through bacterial conjugation, transferring resistance plasmids directly between adjacent cells via a pilus Correct answer.
  4. By mutating host human DNA cells

Explanation

Bacterial conjugation allows direct transfer of extrachromosomal DNA plasmids carrying resistance genes (R-plasmids) between bacterial cells via a conjugation pilus.

Question 12Scientific questions, evidence and quantitative reasoning

Energy Return on Investment (EROI) measures energy output relative to input. If a biofuel production facility yields 120 GJ of net usable fuel energy while consuming 30 GJ of fossil energy inputs, what is its EROI value?

  1. 4.0 Correct answer.
  2. 0.25
  3. 3.0
  4. 90

Explanation

EROI = Energy Output / Energy Input = 120 GJ / 30 GJ = 4.0. An EROI > 1 indicates a net positive energy gain.

Question 13Scientific questions, evidence and quantitative reasoning

During an epidemiological outbreak analysis, 400 individuals test positive for a viral pathogen. If 20 of these confirmed cases die as a result of the infection, what is the Case Fatality Rate (CFR)?

  1. 2.0%
  2. 5.0% Correct answer.
  3. 10.0%
  4. 0.05%

Explanation

Case Fatality Rate (CFR) = (Number of deaths / Confirmed cases) * 100% = (20 / 400) * 100% = 0.05 * 100% = 5.0%.

Question 14Scientific questions, evidence and quantitative reasoning

Silicon photovoltaic solar cells require photons with energy exceeding the semiconductor bandgap energy (Eg = 1.1 eV) to generate electricity. What physical phenomenon describes the excitation of electrons from the valence band to the conduction band upon photon absorption?

  1. Thermoelectric Seebeck effect
  2. Compton scattering effect
  3. Photovoltaic (internal photoelectric) effect Correct answer.
  4. Nuclear magnetic resonance

Explanation

The photovoltaic effect occurs when absorbed photons transfer energy to valence electrons, promoting them across the semiconductor bandgap (Eg = 1.1 eV in silicon) into the conduction band to generate an electric current.

Question 15Matter, materials, reactions and chemical reasoning

A neutral atom of the chlorine-35 isotope (atomic number Z = 17, mass number A = 35) contains which composition of subatomic particles?

  1. 17 protons, 18 neutrons, and 17 electrons Correct answer.
  2. 17 protons, 35 neutrons, and 17 electrons
  3. 18 protons, 17 neutrons, and 18 electrons
  4. 35 protons, 17 neutrons, and 35 electrons

Explanation

The atomic number Z = 17 defines the number of protons in the nucleus, which equals 17. In a neutral atom, the number of electrons equals the number of protons (17). The number of neutrons is calculated as the mass number minus the atomic number: A - Z = 35 - 17 = 18 neutrons.

Question 16Matter, materials, reactions and chemical reasoning

Which statement correctly describes the general periodic trend of electronegativity across the periodic table?

  1. Electronegativity decreases from left to right across a period and increases down a group.
  2. Electronegativity increases from left to right across a period and decreases down a group. Correct answer.
  3. Electronegativity remains constant across a period and decreases down a group.
  4. Electronegativity increases down a group and remains constant across a period.

Explanation

Electronegativity measures an atom's tendency to attract shared electrons in a chemical bond. It increases moving from left to right across a period due to increasing effective nuclear charge, and decreases moving down a group because inner electron shells shield the outer valence electrons.

Question 17Matter, materials, reactions and chemical reasoning

Which characteristic property is typical of metallic substances as explained by the electron sea model?

  1. High brittleness and poor electrical conductivity in the solid state
  2. Low boiling points and discrete molecular structures
  3. High electrical and thermal conductivity due to delocalized valence electrons Correct answer.
  4. Ability to form directional covalent bonds in a rigid lattice

Explanation

According to the metallic bonding model, positive metal cations are surrounded by a mobile 'sea' of delocalized valence electrons. These freely moving electrons allow metals to conduct heat and electricity efficiently in the solid state.

Question 18Matter, materials, reactions and chemical reasoning

What are the stoichiometric coefficients required to balance the complete combustion reaction of propane: C3H8 + x O2 -> y CO2 + z H2O?

  1. x = 3, y = 3, z = 4
  2. x = 4, y = 3, z = 4
  3. x = 5, y = 4, z = 3
  4. x = 5, y = 3, z = 4 Correct answer.

Explanation

Balancing C3H8 + 5 O2 -> 3 CO2 + 4 H2O: 3 carbons yield 3 CO2, 8 hydrogens yield 4 H2O. The right side contains 3*2 + 4*1 = 10 oxygen atoms, requiring 5 O2 molecules. Thus x = 5, y = 3, z = 4.

Question 19Matter, materials, reactions and chemical reasoning

Which phase change process describes the direct transition of a substance from the solid state into the gaseous state without passing through a liquid phase?

  1. Sublimation Correct answer.
  2. Deposition
  3. Vaporization
  4. Condensation

Explanation

Sublimation is the endothermic phase change in which a solid transforms directly into a gas without entering the liquid state (e.g., solid carbon dioxide or iodine). Deposition is the reverse process.

Question 20Matter, materials, reactions and chemical reasoning

What is the pH of a 0.01 M aqueous solution of hydrochloric acid (HCl), assuming complete dissociation?

  1. 1.0
  2. 2.0 Correct answer.
  3. 3.0
  4. 12.0

Explanation

Hydrochloric acid is a strong acid that completely dissociates: [H+] = 0.01 M = 10^-2 M. Calculating pH = -log10[H+] gives -log10(10^-2) = 2.0.

Question 21Matter, materials, reactions and chemical reasoning

In a liquid solution, how is a 'saturated solution' defined at a given temperature and pressure?

  1. A solution that contains less solute than the maximum dissolved amount possible at equilibrium
  2. A solution in which no solvent remains in the liquid state
  3. A solution containing the maximum concentration of dissolved solute in equilibrium with undissolved solute Correct answer.
  4. A solution prepared by mixing equal volumes of two completely immiscible liquids

Explanation

A saturated solution contains the maximum possible concentration of dissolved solute at a specified temperature and pressure, establishing a dynamic equilibrium between dissolved and undissolved solute particles.

Question 22Matter, materials, reactions and chemical reasoning

What is the oxidation state of sulfur (S) in sulfuric acid, H2SO4?

  1. +2
  2. +4
  3. -2
  4. +6 Correct answer.

Explanation

In H2SO4, hydrogen has an oxidation number of +1 (total +2) and oxygen has -2 (total -8). For the neutral compound to have a net charge of 0: (+2) + S + (-8) = 0, which yields S = +6.

Question 23Matter, materials, reactions and chemical reasoning

Using the ideal gas law (PV = nRT), calculate the volume occupied by 0.50 moles of nitrogen gas (N2) at a pressure of 1.0 atm and a temperature of 300 K. (R = 0.0821 L*atm/(mol*K)).

  1. 12.3 L Correct answer.
  2. 24.6 L
  3. 6.15 L
  4. 11.2 L

Explanation

Applying PV = nRT: V = (n * R * T) / P = (0.50 mol * 0.0821 L*atm/(mol*K) * 300 K) / 1.0 atm = 12.315 L, which rounds to 12.3 L.

Question 24Matter, materials, reactions and chemical reasoning

What mass of sodium chloride (NaCl, molar mass = 58.5 g/mol) is required to prepare 250 mL of a 0.50 M aqueous solution?

  1. 14.6 g
  2. 7.31 g Correct answer.
  3. 29.3 g
  4. 3.65 g

Explanation

Moles of NaCl needed = Molarity * Volume in liters = 0.50 mol/L * 0.250 L = 0.125 moles. Mass = moles * molar mass = 0.125 mol * 58.5 g/mol = 7.3125 g, which rounds to 7.31 g.

Question 25Matter, materials, reactions and chemical reasoning

In the reaction CH4 + 2 O2 -> CO2 + 2 H2O, what mass of carbon dioxide (CO2, molar mass = 44 g/mol) is produced by the complete combustion of 16.0 g of methane (CH4, molar mass = 16 g/mol)?

  1. 22.0 g
  2. 32.0 g
  3. 44.0 g Correct answer.
  4. 88.0 g

Explanation

Moles of CH4 = 16.0 g / 16.0 g/mol = 1.0 mol. From reaction stoichiometry, 1 mol CH4 produces 1 mol CO2. Mass of CO2 = 1.0 mol * 44.0 g/mol = 44.0 g.

Question 26Matter, materials, reactions and chemical reasoning

Which statement correctly describes an exothermic chemical reaction occurring at constant pressure?

  1. The reaction absorbs heat from the surroundings, resulting in a positive enthalpy change (Delta H > 0).
  2. The enthalpy of the products is greater than the enthalpy of the reactants.
  3. The reaction requires continuous external heating to proceed to completion.
  4. The reaction releases thermal energy to the surroundings, resulting in a negative enthalpy change (Delta H < 0). Correct answer.

Explanation

Exothermic reactions transfer heat to their surroundings because the potential energy of the products is lower than that of the reactants. Consequently, the enthalpy change is negative (Delta H < 0).

Question 27Matter, materials, reactions and chemical reasoning

For the gaseous equilibrium system N2(g) + 3 H2(g) <=> 2 NH3(g) (Delta H < 0), what shift occurs when the total pressure on the container is increased at constant temperature?

  1. The equilibrium shifts to the right (toward products) to reduce the total number of gas moles. Correct answer.
  2. The equilibrium shifts to the left (toward reactants) to increase gas volume.
  3. The equilibrium remains unchanged because pressure does not affect gas reactions.
  4. The equilibrium constant Keq increases proportionally with total pressure.

Explanation

According to Le Chatelier's principle, increasing total pressure shifts the equilibrium toward the side with fewer moles of gas. The reactant side has 1 + 3 = 4 gas moles, while the product side has 2 gas moles, so the reaction shifts right.

Question 28Matter, materials, reactions and chemical reasoning

Which organic functional group is characterized by a carbonyl group (C=O) bonded directly to an oxygen atom that is attached to an alkyl chain (R-COO-R')?

  1. Ether
  2. Ester Correct answer.
  3. Carboxylic acid
  4. Ketone

Explanation

An ester contains a carbonyl group bonded to an alkoxy group (-O-R'). They are commonly formed by the condensation reaction between a carboxylic acid and an alcohol.

Question 29Matter, materials, reactions and chemical reasoning

Magnesium reacts with oxygen according to 2 Mg + O2 -> 2 MgO. If 0.40 moles of Mg are mixed with 0.30 moles of O2, which reactant is limiting and how many moles of MgO are produced?

  1. O2 is limiting; 0.60 moles of MgO are produced.
  2. Mg is limiting; 0.30 moles of MgO are produced.
  3. Mg is limiting; 0.40 moles of MgO are produced. Correct answer.
  4. O2 is limiting; 0.40 moles of MgO are produced.

Explanation

From the stoichiometry, 0.40 moles of Mg require 0.20 moles of O2 (0.40 / 2). Since 0.30 moles of O2 are available, O2 is in excess and Mg is the limiting reactant. 0.40 mol of Mg yields 0.40 mol of MgO.

Question 30Matter, materials, reactions and chemical reasoning

What volume of concentrated 6.0 M HCl stock solution is required to prepare 500 mL of a 0.30 M HCl solution by dilution?

  1. 100 mL
  2. 50 mL
  3. 15 mL
  4. 25 mL Correct answer.

Explanation

Using the dilution equation M1 * V1 = M2 * V2: (6.0 M) * V1 = (0.30 M) * (500 mL). Solving for V1 = (0.30 * 500) / 6.0 = 150 / 6.0 = 25 mL.

Question 31Matter, materials, reactions and chemical reasoning

A radioactive sample of Iodine-131 has a half-life of 8.0 days. Starting with an initial mass of 80.0 g, what mass of Iodine-131 remains after 24.0 days?

  1. 10.0 g Correct answer.
  2. 20.0 g
  3. 5.0 g
  4. 40.0 g

Explanation

The number of elapsed half-lives is n = 24.0 days / 8.0 days = 3 half-lives. Remaining mass = Initial Mass * (1/2)^n = 80.0 g * (1/2)^3 = 80.0 / 8 = 10.0 g.

Question 32Matter, materials, reactions and chemical reasoning

Why does water (H2O) possess a significantly higher boiling point (100 °C) than hydrogen sulfide (H2S, boiling point -60 °C), despite H2S having a larger molar mass?

  1. H2O molecules are held together by strong covalent network bonds in the liquid state.
  2. H2O forms strong intermolecular hydrogen bonds due to O-H bond polarity, whereas H2S exhibits only weaker dipole-dipole and London forces. Correct answer.
  3. H2S undergoes spontaneous thermal decomposition at room temperature.
  4. H2O molecules exhibit weaker London dispersion forces than H2S.

Explanation

Oxygen is highly electronegative, creating strong O-H hydrogen bonding between H2O molecules. Hydrogen sulfide (H2S) lacks hydrogen bonding because sulfur is less electronegative, resulting in weaker intermolecular forces and a lower boiling point.

Question 33Matter, materials, reactions and chemical reasoning

In the reduction half-reaction of permanganate ion in acidic solution: MnO4- + 8 H+ + n e- -> Mn2+ + 4 H2O, what is the number of electrons (n) gained per manganese atom?

  1. 2
  2. 3
  3. 5 Correct answer.
  4. 7

Explanation

In MnO4-, manganese has an oxidation state of +7. In Mn2+, manganese has an oxidation state of +2. The change in oxidation state is (+7) - (+2) = 5, representing a gain of 5 electrons (n = 5).

Question 34Matter, materials, reactions and chemical reasoning

What key feature distinguishes condensation polymerization from addition polymerization in polymer chemistry?

  1. Addition polymerization forms cross-linked networks, whereas condensation forms linear chains.
  2. Addition polymerization requires monomers containing hydroxyl and carboxyl functional groups.
  3. Condensation polymerization proceeds without breaking chemical bonds in the monomers.
  4. Condensation polymerization releases a small molecular byproduct (such as H2O or HCl) during chain formation. Correct answer.

Explanation

Condensation polymerization occurs when bifunctional monomers react to form polymer linkages while eliminating a small byproduct molecule (e.g., water in polyester synthesis). Addition polymerization involves opening double bonds without forming byproducts.

Question 35Matter, materials, reactions and chemical reasoning

Calculate the pH of a 0.10 M aqueous solution of acetic acid (CH3COOH), given its acid dissociation constant Ka = 1.8 x 10^-5. (Assume x is negligible compared to 0.10 M).

  1. 2.87 Correct answer.
  2. 1.00
  3. 4.74
  4. 3.42

Explanation

For a weak acid: [H+] = sqrt(Ka * C0) = sqrt(1.8 x 10^-5 * 0.10) = sqrt(1.8 x 10^-6) = 1.34 x 10^-3 M. Calculating pH = -log10(1.34 x 10^-3) = 2.87.

Question 36Matter, materials, reactions and chemical reasoning

Calcium carbonate decomposes thermally according to CaCO3(s) -> CaO(s) + CO2(g). What volume of CO2 gas is collected at 300 K and 2.0 atm from the complete decomposition of 10.0 g of CaCO3? (Molar mass CaCO3 = 100 g/mol; R = 0.0821 L*atm/(mol*K)).

  1. 2.46 L
  2. 1.23 L Correct answer.
  3. 0.615 L
  4. 4.92 L

Explanation

Moles of CaCO3 = 10.0 g / 100 g/mol = 0.10 mol, yielding 0.10 mol CO2. Applying PV = nRT: V = (0.10 * 0.0821 * 300) / 2.0 = 2.463 / 2.0 = 1.23 L.

Question 37Matter, materials, reactions and chemical reasoning

Calculate the standard reaction enthalpy (Delta H°rxn) for the oxidation of carbon monoxide: 2 CO(g) + O2(g) -> 2 CO2(g), given Delta H°f[CO(g)] = -110.5 kJ/mol and Delta H°f[CO2(g)] = -393.5 kJ/mol.

  1. -283.0 kJ
  2. +566.0 kJ
  3. -566.0 kJ Correct answer.
  4. -504.0 kJ

Explanation

Delta H°rxn = Sum(n * Delta H°f[products]) - Sum(m * Delta H°f[reactants]) = [2 * (-393.5)] - [2 * (-110.5) + 1 * (0)] = -787.0 - (-221.0) = -566.0 kJ.

Question 38Matter, materials, reactions and chemical reasoning

During the electrolysis of a Cu2+ solution, a constant electric current of 5.0 A is passed through the cell for 1930 seconds. What mass of metallic copper (Cu, molar mass = 63.55 g/mol, Faraday constant F = 96,500 C/mol e-) is deposited at the cathode?

  1. 6.36 g
  2. 1.59 g
  3. 12.7 g
  4. 3.18 g Correct answer.

Explanation

Total charge Q = I * t = 5.0 A * 1930 s = 9650 C. Moles of electrons = Q / F = 9650 / 96500 = 0.10 mol e-. Reduction reaction: Cu2+ + 2 e- -> Cu, so moles of Cu = 0.10 / 2 = 0.050 mol Cu. Mass = 0.050 mol * 63.55 g/mol = 3.1775 g, which rounds to 3.18 g.

Question 39Matter, materials, reactions and chemical reasoning

How many constitutional (structural) isomers exist for the alkane with molecular formula C5H12?

  1. 3 Correct answer.
  2. 4
  3. 5
  4. 2

Explanation

Pentane (C5H12) has exactly 3 constitutional isomers: pentane (straight chain), 2-methylbutane (isopentane), and 2,2-dimethylpropane (neopentane).

Question 40Forces, energy, fields, waves and modern physical models

Calculate the kinetic energy of a 1200 kg automobile traveling along a straight road at a constant speed of 20 m/s.

  1. 240 kJ Correct answer.
  2. 120 kJ
  3. 480 kJ
  4. 24 kJ

Explanation

Kinetic energy Ek = 0.5 * m * v^2 = 0.5 * 1200 kg * (20 m/s)^2 = 600 * 400 = 240,000 J = 240 kJ.

Question 41Forces, energy, fields, waves and modern physical models

What net force is required to accelerate an 8.0 kg object across a frictionless horizontal surface at a rate of 2.5 m/s^2?

  1. 3.2 N
  2. 20 N Correct answer.
  3. 10.5 N
  4. 50 N

Explanation

Applying Newton's second law F = m * a: F = 8.0 kg * 2.5 m/s^2 = 20 N.

Question 42Forces, energy, fields, waves and modern physical models

What is the gravitational potential energy of a 4.0 kg spherical weight held at a height of 15 m above ground level? (g = 9.8 m/s^2).

  1. 60 J
  2. 392 J
  3. 588 J Correct answer.
  4. 1176 J

Explanation

Gravitational potential energy Ep = m * g * h = 4.0 kg * 9.8 m/s^2 * 15 m = 588 J.

Question 43Forces, energy, fields, waves and modern physical models

A sound wave travels through air at a temperature of 20 °C with a frequency of 440 Hz and a wavelength of 0.773 m. What is the propagation speed of the sound wave?

  1. 569 m/s
  2. 220 m/s
  3. 172 m/s
  4. 340 m/s Correct answer.

Explanation

The wave speed equation is v = f * lambda = 440 s^-1 * 0.773 m = 340.12 m/s, which rounds to 340 m/s.

Question 44Forces, energy, fields, waves and modern physical models

What electrical current flows through a metallic wire if 150 Coulombs of charge pass through its cross-section in 30 seconds?

  1. 5.0 A Correct answer.
  2. 4500 A
  3. 0.20 A
  4. 15 A

Explanation

Electric current is defined as charge per unit time: I = Q / t = 150 C / 30 s = 5.0 A.

Question 45Forces, energy, fields, waves and modern physical models

How much thermal energy is required to raise the temperature of 2.0 kg of liquid water by 10 °C? (Specific heat capacity of water c = 4184 J/(kg*°C)).

  1. 20.9 kJ
  2. 83.7 kJ Correct answer.
  3. 41.8 kJ
  4. 418.4 kJ

Explanation

Heat transfer Q = m * c * Delta T = 2.0 kg * 4184 J/(kg*°C) * 10 °C = 83,680 J = 83.7 kJ.

Question 46Forces, energy, fields, waves and modern physical models

What potential difference (voltage) must be applied across a 24 ohm resistor to produce an electric current of 0.50 A?

  1. 48 V
  2. 6.0 V
  3. 12 V Correct answer.
  4. 24 V

Explanation

Applying Ohm's law V = I * R: V = 0.50 A * 24 ohms = 12 V.

Question 47Forces, energy, fields, waves and modern physical models

An automobile traveling along a straight highway at 25 m/s applies brakes and decelerates uniformly at -5.0 m/s^2 until coming to a complete stop. What is the total stopping distance?

  1. 125 m
  2. 31.3 m
  3. 50.0 m
  4. 62.5 m Correct answer.

Explanation

Using kinematic equation v^2 = v0^2 + 2 * a * d: 0 = (25)^2 + 2 * (-5.0) * d => 0 = 625 - 10 * d => 10 * d = 625 => d = 62.5 m.

Question 48Forces, energy, fields, waves and modern physical models

A worker pulls a crate across a horizontal floor over a distance of 10 m by exerting a constant force of 100 N at an angle of 60° above the horizontal. Calculate the work done by the worker. (cos 60° = 0.50).

  1. 500 J Correct answer.
  2. 1000 J
  3. 866 J
  4. 250 J

Explanation

Mechanical work W = F * d * cos(theta) = 100 N * 10 m * cos(60°) = 1000 * 0.50 = 500 J.

Question 49Forces, energy, fields, waves and modern physical models

A small rock is dropped from rest from the top of a cliff of height h = 20 m. Neglecting air resistance, what is its impact velocity just before hitting the ground? (g = 9.8 m/s^2).

  1. 14.0 m/s
  2. 19.8 m/s Correct answer.
  3. 392 m/s
  4. 28.0 m/s

Explanation

By conservation of energy m*g*h = 0.5*m*v^2 => v = sqrt(2 * g * h) = sqrt(2 * 9.8 * 20) = sqrt(392) = 19.8 m/s.

Question 50Forces, energy, fields, waves and modern physical models

An electric space heater rated at 1500 W operates continuously for 4.0 hours. How much electrical energy does it consume in kilowatt-hours (kWh)?

  1. 3.75 kWh
  2. 600 kWh
  3. 6.0 kWh Correct answer.
  4. 15 kWh

Explanation

Power P = 1500 W = 1.5 kW. Energy E = Power * Time = 1.5 kW * 4.0 h = 6.0 kWh.