O Level Physics (5054) — MCQs & Practice Questions

A base unit is one of the seven independent SI units, such as the metre. A derived unit is built from base units by multiplication or division, such as the newton, 1 N = 1 kg m s⁻².

The smallest measurement the instrument can read — the value of one division on its scale. A metre rule has a least count of 1 mm; a vernier calliper, 0.1 mm; a screw gauge, 0.01 mm.

Random errors scatter either side of the true value, so averaging makes them partly cancel. A single reading may happen to be one of the extreme ones.

1. Convert: 12.5 cm = 0.125 m, 0.1 cm = 0.001 mdivide by 100[1]
2. Percentage uncertainty = (Δl / l) × 100 = (0.1 / 12.5) × 100same units top and bottom, so the conversion cancels[1]
3. = 0.8%[1]

0.125 ± 0.001 m, or 0.8%

1. 0.51 mm is anomalous — it lies well away from the others[1]
2. It should be excluded from the mean, but reported rather than deletedthe reporting half is the mark most often missed[1]
3. Mean = (0.42 + 0.43 + 0.42 + 0.43) / 4four readings, not five[1]
4. = 0.425 ≈ 0.43 mm[1]

(a) 0.51 mm, excluded but reported (b) 0.43 mm

1. Selects v² = u² + 2asthe equation without t, since t is not given in part (a)[1]
2. 10.0² = 4.0² + 2 × a × 42 → 100 = 16 + 84a → a = 1.0 m s⁻²unit required for the mark[1]
3. Selects v = u + at (or s = ½(u+v)t)[1]
4. 10.0 = 4.0 + 1.0t → t = 6.0 s[1]

(a) 1.0 m s⁻² (b) 6.0 s

1. Uses s = ut + ½at² with u = 0"dropped from rest" is what tells you u = 0[1]
2. s = ½ × 9.81 × 3.2² = 50.2 ≈ 50 m[1]
3. Uses v = u + ator v² = u² + 2as[1]
4. v = 9.81 × 3.2 = 31.4 ≈ 31 m s⁻¹[1]
5. The actual speed would be lower / the stone would reach terminal velocitya statement about direction of change is enough[1]

(a) 50 m (b) 31 m s⁻¹ (c) the speed would be less

1. Acceleration = gradient = (20 − 0) / 40gradient of a velocity–time graph is acceleration[1]
2. = 0.50 m s⁻²[1]
3. Recognises distance = area under the graphthis is the mark most often missed[1]
4. Triangle ½ × 40 × 20 = 400; rectangle 60 × 20 = 1200; triangle ½ × 30 × 20 = 300all three areas needed[1]
5. Total = 1900 m[1]
6. Average speed = 1900 / 130 = 14.6 ≈ 15 m s⁻¹total distance ÷ total time, not the mean of the velocities[1]

(a) 0.50 m s⁻² (b) 1900 m (c) 15 m s⁻¹

1. Uses vertical motion with u_y = 0: 45 = ½ × 10 × t²"thrown horizontally" means the initial vertical velocity is zero[1]
2. t² = 9.0, t = 3.0 s[1]
3. Uses s_x = u_x t with constant horizontal velocity[1]
4. s_x = 15 × 3.0 = 45 m[1]
5. Horizontal and vertical motion are independent / gravity acts only vertically, so the vertical motion is unaffected by the horizontal velocity[1]

(a) 3.0 s (b) 45 m (c) the two components are independent

1. Displacement is the straight-line distance from the starting point to the finishing point[1]
2. …together with its direction / it is a vector quantitythe direction is required for the second mark[1]
3. Any curved or non-straight path, e.g. a runner going round a bend, a car following a winding roada full circular lap, where displacement is zero, also earns this[1]

Distance is the total length of the path travelled, a scalar. Displacement is the straight line from start to finish together with its direction, a vector.

Yes. A ball thrown vertically upward is momentarily at rest at the top of its flight, but gravity still acts, so its acceleration is g downward.

1. Uses a = (v − u)/t = (0 − 25)/5.0[1]
2. a = −5.0 m s⁻², a deceleration of 5.0 m s⁻²the negative sign or the word deceleration, not both required[1]
3. Uses s = ½(u + v)t or v² = u² + 2as[1]
4. s = ½(25 + 0) × 5.0 = 62.5 m[1]

deceleration 5.0 m s⁻², distance 62.5 m

1. Uses W = mg[1]
2. W = 25 × 9.8 = 245 N[1]
3. W = 25 × 1.6 = 40 N[1]
4. Mass is 25 kgunchanged[1]
5. Mass is the quantity of matter and does not depend on gravitational field strengththe explanation mark[1]

(a) 245 N (b) 40 N (c) 25 kg — mass does not depend on location

1. The spring balance reading changes; the beam balance reading does not[1]
2. A spring balance measures force / weight, which depends on g[1]
3. g is smaller on the Moon, so the weight and hence the reading is smaller[1]
4. A beam balance compares two masses, and both are affected equally by the change in g, so the comparison is unaffectedthe harder mark[1]

1. Rearranges to m = W/g[1]
2. m = 96 / 3.2 = 30 kg[1]
3. On Earth W = 30 × 9.8 = 294 Nthe mass is the quantity that carries across[1]

m = 30 kg, and 294 N on Earth

The force per unit mass acting on a body placed in the field, g = W/m. Unit: N kg⁻¹.

The tendency of a body to resist a change in its state of motion. It is measured by its mass.

1. Mass is the quantity of matter in the satellite, a scalar measured in kilograms[1]
2. It is the same wherever the satellite is taken[1]
3. Weight is the gravitational force on that mass, a vector measured in newtons[1]
4. It changes with the gravitational field strength of the location[1]
5. Uses W = mg[1]
6. W = 400 × 9.8 = 3920 N[1]
7. Rearranges to g = W/m[1]
8. g = 1480 / 400mass is unchanged at 400 kg[1]
9. g = 3.7 N kg⁻¹roughly Mars[1]

(b) 3920 N (c) 3.7 N kg⁻¹

1. Volume = 0.20 × 0.10 × 0.050 = 1.0 × 10⁻³ m³converting every length to metres first[1]
2. Density = 0.80 / 1.0 × 10⁻³ = 800 kg m⁻³[1]
3. Weight = mg = 0.80 × 10 = 8.0 Npressure needs force, and the force here is the weight[1]
4. Largest face area = 0.20 × 0.10 = 0.020 m²largest face gives the lowest pressure[1]
5. Pressure = 8.0 / 0.020 = 400 Pa[1]

(a) 800 kg m⁻³ (b) 400 Pa

1. Uses p = ρgh[1]
2. p = 1000 × 10 × 12 = 1.2 × 10⁵ Paunit required[1]
3. No effect / the pressure is unchanged[1]
4. Pressure in a liquid depends only on depth, density and g — not on the shape or width of the containerthe reasoning mark; the statement alone scores 1 of 2[1]

(a) 1.2 × 10⁵ Pa (b) no change — pressure depends only on depth

1. Extension = 12.0 − 8.0 = 4.0 cm = 0.040 mextension, not total length — the mark most often lost on this topic[1]
2. k = F/x = 5.0 / 0.040 = 125 N m⁻¹[1]
3. New extension = 8.0 / 125 = 0.064 m = 6.4 cm[1]
4. New length = 8.0 + 6.4 = 14.4 cmadding the natural length back on[1]

(a) 125 N m⁻¹ (b) 14.4 cm

Mass per unit volume, ρ = m/V. SI unit: kg m⁻³.

Broad feet spread the camel's weight over a larger area, so the pressure on the sand is smaller and it does not sink.

The extension of a spring is directly proportional to the load applied, provided the limit of proportionality is not exceeded.

1. Uses p = ρgh[1]
2. p = 800 × 10 × 1.5 = 12 000 Paunit required[1]
3. Rearranges p = F/A to F = pA[1]
4. F = 12 000 × 2.0 = 24 000 N[1]

p = 1.2 × 10⁴ Pa, F = 2.4 × 10⁴ N

For every action there is an equal and opposite reaction. The two forces are of the same type and act on different bodies.

By Newton's first law the passenger continues moving at the same velocity because no resultant force acts on them; the bus decelerates beneath them, so they move forward relative to it.

The product of mass and velocity, p = mv. A vector quantity. SI unit: kg m s⁻¹.

1. States conservation of momentum: total before = total after[1]
2. Before: p = 2.0 × 3.0 + 4.0 × 0 = 6.0 kg m s⁻¹[1]
3. After: combined mass = 6.0 kg, so 6.0 = 6.0 × vthey stick together, so they share one velocity[1]
4. v = 1.0 m s⁻¹ in the original directiondirection expected for full marks[1]

1.0 m s⁻¹ in the direction of the original motion

1. Resultant force = 15 − 6.0 = 9.0 Nfriction opposes, so it subtracts[1]
2. Uses F = ma[1]
3. a = F/m = 9.0 / 3.0[1]
4. a = 3.0 m s⁻²unit required[1]

3.0 m s⁻²

1. Uses p = mv[1]
2. p = 1200 × 15 = 18 000 kg m s⁻¹the stationary car contributes nothing[1]
3. Applies conservation: total after = 18 000 kg m s⁻¹[1]
4. Combined mass 2000 kg, so v = 18 000 / 2000 = 9.0 m s⁻¹[1]
5. Kinetic energy is not conserved[1]
6. Inelastic collisionobjects sticking together is always inelastic[1]

(a) 1.8 × 10⁴ kg m s⁻¹ (b) 9.0 m s⁻¹ (c) not conserved; inelastic

1. Total momentum before is zeronothing is moving[1]
2. 0 = 0.020 × 400 + 4.0 × v[1]
3. v = −8.0 / 4.0 = −2.0 m s⁻¹, i.e. 2.0 m s⁻¹ backwardsdirection required[1]
4. The rifle's momentum must equal the bullet's in size and be opposite in direction[1]
5. Since p = mv is fixed, a larger m gives a smaller v[1]

2.0 m s⁻¹ backwards

1. Takes the initial direction as positive, so the rebound velocity is −8.0 m s⁻¹the sign is the whole question[1]
2. Δp = m(v − u) = 0.15 × (−8.0 − 12) = −3.0 kg m s⁻¹a change of 20 m s⁻¹, not 4[1]
3. Uses F = Δp/Δt[1]
4. F = −3.0 / 0.050 = −60 N, i.e. 60 N away from the wall[1]

60 N, directed away from the wall

The total momentum of a system before an interaction equals the total momentum after it, provided no resultant external force acts on the system.

It increases the time over which the ball is brought to rest. Since F = Δp/Δt and the change in momentum is fixed, a longer time means a smaller force on the hands.

1. Uses Δp = m(v − u) with u = 0the ball starts at rest on the tee[1]
2. Δp = 0.045 × 60 = 2.7 kg m s⁻¹[1]
3. Converts the time: 0.50 ms = 5.0 × 10⁻⁴ s[1]
4. Uses F = Δp/Δt[1]
5. F = 2.7 / 5.0 × 10⁻⁴ = 5400 N[1]
6. Applies conservation of momentum to club and ball together[1]
7. Before: 0.30 × 70 = 21 kg m s⁻¹the ball contributes nothing[1]
8. After: 21 = 0.30 × v + 2.7[1]
9. v = 18.3 / 0.30 = 61 m s⁻¹[1]

(a) 2.7 kg m s⁻¹ (b) 5400 N (c) 61 m s⁻¹

Work = force × distance moved in the direction of the force, W = Fs cos θ. It is zero when the force is perpendicular to the motion, since cos 90° = 0.

Energy cannot be created or destroyed, only transferred from one store to another. The total energy of a closed system remains constant.

No. Energy is transferred to heat and sound in the ball and the floor at each bounce, so less remains as gravitational potential energy. The total is unchanged.

1. Uses E = mghthe useful energy is the gravitational potential energy gained[1]
2. E = 300 × 10 × 12 = 36 000 J[1]
3. Uses P = E/t[1]
4. P = 36 000 / 40 = 900 Wunit required[1]

900 W

1. Uses KE = ½mv²[1]
2. KE = ½ × 1200 × 20² = 240 000 Jsquare the velocity before multiplying[1]
3. Gain in KE = 240 000 J since it started from rest[1]
4. P = 240 000 / 8.0 = 30 000 W = 30 kW[1]

2.4 × 10⁵ J and 30 kW

1. At the centre of gravity, which for a uniform beam is its midpoint, 1.0 m from the left end"uniform" is the word that tells you this[1]
2. Takes moments about the pivot; the beam's weight acts 1.0 − 0.50 = 0.50 m to the right of it[1]
3. Clockwise = anticlockwise: 40 × 0.50 = W × 0.50the load acts 0.50 m to the left of the pivot[1]
4. W = 40 N[1]

(a) at the midpoint, 1.0 m from the left end (b) W = 40 N

1. Passengers upstairs raise the centre of gravity of the bus[1]
2. A higher centre of gravity means a smaller tilt is needed before the vertical line through it falls outside the base / wheelbasethis is the key reasoning mark[1]
3. So the bus topples at a smaller angle / is less stable[1]

1. Recognises that only the perpendicular component turns the nutor equivalently uses the perpendicular distance[1]
2. Perpendicular component = 12 sin 30° = 6.0 N[1]
3. Moment = 6.0 × 0.25 = 1.5 N munit required[1]

1.5 N m

The turning effect of a force about a pivot, equal to force × perpendicular distance from the pivot to the line of action. SI unit: the newton metre, N m.

They are different quantities. Work is force acting along a displacement; a moment is force acting across a distance from a pivot. Sharing base units does not make them the same thing.

ΣF = 0 — no resultant force, so it does not accelerate. Σ moments = 0 — no resultant turning effect, so it does not rotate.

1. Left distance = 50 − 20 = 30 cm = 0.30 mdistance from the pivot, not from the end of the rule[1]
2. Anticlockwise moment = 3.0 × 0.30 = 0.90 N m[1]
3. Right distance = 70 − 50 = 20 cm = 0.20 m; for balance W₂ × 0.20 = 0.90principle of moments[1]
4. W₂ = 4.5 Nunit required[1]

4.5 N

1. Brownian motion[1]
2. The smoke particles are bombarded by air molecules[1]
3. The bombardment is uneven / random, so the resultant force keeps changing directionthe mark that separates a full answer[1]
4. Air molecules are very smalltoo small to see individually[1]
5. They are moving rapidly and randomly[1]

1. The pressure increases[1]
2. The particles gain kinetic energy and move faster[1]
3. They collide with the walls more frequently[1]
4. Each collision exerts a greater force, so the total force per unit area risesboth "more often" and "harder" are needed for full marks[1]

1. Uses p₁V₁ = p₂V₂temperature constant, so Boyle's law applies[1]
2. 3.0 × 10⁵ × 2.0 = 1.0 × 10⁵ × V₂[1]
3. V₂ = 6.0 cm³lower pressure, larger bubble — check the direction[1]

6.0 cm³

In a gas the particles are far apart with large spaces between them, which can be reduced. In a liquid the particles are already touching, so there is no space to remove.

Raise its temperature, so the particles move faster and collide harder and more often. Or reduce its volume, so the same particles strike a smaller area more frequently.

1. Particles move rapidly and randomly, colliding with the walls[1]
2. Each collision exerts a small force on the wall[1]
3. Pressure is the total force per unit area of wall[1]
4. Uses p₁V₁ = p₂V₂, stating that the temperature is constant[1]
5. 2.0 × 10⁵ × 0.50 = p₂ × 0.20[1]
6. p₂ = 5.0 × 10⁵ Pa[1]
7. The pressure would increase[1]
8. The particles gain kinetic energy, so they hit the walls harder and more often[1]

(b) 5.0 × 10⁵ Pa (c) pressure rises

1. Uses E = mcΔθ with Δθ = 70 °C88 − 18, not 88[1]
2. E = 1.5 × 4200 × 70 = 4.41 × 10⁵ J[1]
3. Uses t = E/P with P = 2000 Wconverting kW to W[1]
4. t = 441000 / 2000 = 220 saccept 220.5 s[1]
5. Energy is lost to the surroundings / the container is also heatedeither reason accepted[1]

(a) 4.4 × 10⁵ J (b) 220 s (c) heat lost to surroundings

1. Temperature rises from −10 °C to 0 °C[1]
2. Horizontal section at 0 °C while the ice melts[1]
3. Temperature rises from 0 °C to 100 °C[1]
4. Longer horizontal section at 100 °C while the water boilsthe boiling plateau must be longer than the melting one[1]
5. During the flat sections the energy supplied breaks bonds between particles rather than raising kinetic energythe explanation mark[1]

1. Heating makes particles vibrate more and push further apart, so each metal expands[1]
2. The two metals expand by different amounts for the same temperature risethis is the essential point[1]
3. The strip bends toward the metal that expands less[1]
4. Used in a thermostat / fire alarm / oven switchany valid use[1]

Temperature is the average kinetic energy of the particles, measured in °C or K. Heat is the total thermal energy of all the particles, measured in joules, and depends on how many there are.

The two metals expand by different amounts for the same temperature rise, so the strip curves toward the metal that expands less.

The energy supplied is used to break the bonds holding the particles in the lattice, not to increase their kinetic energy. Since temperature measures kinetic energy, it does not change.

1. Recognises two stages: melting, then warminga single-stage answer cannot score more than two[1]
2. Melting: E₁ = mL = 0.20 × 3.34 × 10⁵ = 6.68 × 10⁴ J[1]
3. Warming: E₂ = mcΔθ = 0.20 × 4200 × 20[1]
4. E₂ = 1.68 × 10⁴ J[1]
5. Total = 6.68 × 10⁴ + 1.68 × 10⁴ = 8.36 × 10⁴ Jadding the two stages[1]

8.36 × 10⁴ J

1. A vacuum contains no particles[1]
2. So there is no conduction and no convection through itboth must be named[1]
3. Silvered surfaces are poor emitters of infrared radiation[1]
4. And good reflectors, so radiation is reflected back into the liquid[1]
5. The stopper prevents convection currents / evaporation carrying energy away[1]
6. And is made of an insulating material, so conduction through the top is small[1]

1. Convection[1]
2. Air near the radiator is heated and expands[1]
3. Its density decreases, so it risesthe density step is the mark most often skipped[1]
4. Cooler denser air sinks to replace it, setting up a convection current[1]

1. Metal is a much better conductor than wood[1]
2. It conducts thermal energy away from the hand quickly[1]
3. The rapid energy loss from the skin is what is sensed as cold — the rail is not actually colderthe point of the question[1]

Water heated at the bottom expands, becomes less dense and rises, while cooler denser water sinks to replace it. This convection current heats the whole kettle.

A white, shiny surface is a poor absorber and a good reflector of infrared radiation, so less energy is absorbed and the interior stays cooler.

1. Matt black is the best absorber of infrared radiation[1]
2. So the panel absorbs as much of the Sun's energy as possible[1]
3. Metal is a good conductor[1]
4. So energy passes quickly from the panel surface to the water in the pipes[1]
5. The glass traps a layer of air above the panel[1]
6. Preventing convection currents from carrying energy away[1]
7. Heated water expands, becomes less dense and rises[1]
8. Cooler denser water from the tank sinks to replace it, forming a convection current[1]

Wavelength is the distance between two neighbouring points that are in phase, for example crest to crest. Frequency is the number of complete waves passing a fixed point each second.

In a transverse wave the vibration is perpendicular to the direction of travel, for example light. In a longitudinal wave it is parallel to the direction of travel, for example sound.

The frequency stays the same. The speed decreases and, since v = fλ, the wavelength decreases in proportion.

1. Uses λ = length ÷ number of waves[1]
2. λ = 3.0 / 15 = 0.20 m[1]
3. Uses v = fλ[1]
4. v = 12 × 0.20 = 2.4 m s⁻¹[1]

λ = 0.20 m, v = 2.4 m s⁻¹

1. The waves spread out after passing through the gap[1]
2. This is diffraction[1]
3. The wavelength and frequency are unchanged; only the shape of the wavefront changes[1]
4. The waves spread out more[1]
5. Because the gap width is closer to the wavelengthmaximum spreading when gap ≈ λ[1]
6. Converts 25 mm = 0.025 m[1]
7. Uses v = fλ[1]
8. v = 8.0 × 0.025 = 0.20 m s⁻¹[1]

(c) 0.20 m s⁻¹

1. The waves change direction at the boundary[1]
2. They bend towards the normal[1]
3. The waves travel more slowly in the shallow water[1]
4. The end of each wavefront entering the shallow region slows first[1]
5. So the wavefront pivots, changing the direction of travel[1]
6. The direction does not change[1]
7. Because the whole wavefront slows at the same instant, so there is nothing to pivot aboutthe wavelength still shortens[1]

1. Uses n = sin i / sin r[1]
2. sin r = sin 40° / 1.50 = 0.643 / 1.50 = 0.4285[1]
3. r = 25.4°accept 25°[1]
4. Uses sin c = 1/n = 1/1.50 = 0.667, giving c = 41.8°accept 42°[1]
5. Light must travel from a denser to a less dense medium[1]
6. The angle of incidence must exceed the critical angleboth conditions needed[1]

(a) 25.4° (b) 41.8° (c) denser → less dense, and i > c

1. Light strikes the boundary between the core and the cladding[1]
2. The core is optically denser than the cladding[1]
3. The angle of incidence is greater than the critical angle[1]
4. So total internal reflection occurs, repeatedly, and the light follows the fibre[1]

1. Real and invertedthe object lies between F and 2F[1]
2. It is also magnified[1]
3. A projector (or a film projector / slide projector)[1]
4. At 5 cm the object is inside F, so the image becomes virtual, upright and magnifieda magnifying glass[1]

(a) real, inverted, magnified (b) projector (c) becomes virtual, upright and magnified

A real image is formed where light rays actually meet and can be caught on a screen. A virtual image is formed where rays only appear to come from and cannot be projected.

Light from the submerged part refracts as it leaves the water and enters the air, bending away from the normal. The eye assumes light travels in straight lines, so the straw appears displaced.

1. Uses sin c = 1/n[1]
2. sin c = 1/1.33 = 0.752[1]
3. c = 48.8°accept 49°[1]
4. Total internal reflection occurs[1]
5. Because 60° is greater than the critical angle of 48.8°[1]
6. And the light is travelling from the denser medium to the less dense oneboth conditions[1]
7. Light repeatedly totally internally reflects at the core–cladding boundary, so it follows the fibre even around bends[1]
8. Advantage: much higher data capacity / less signal loss over distance / no electrical interferenceany one[1]
9. Second valid point about the mechanism or the advantage[1]

(a) 48.8° (b) total internal reflection (c) repeated TIR at the core–cladding boundary

1. Radio, microwave, infrared, visible, ultraviolet, X-ray, gammatwo marks for the full correct order; one for a mostly correct order[2]
2. 3.0 × 10⁸ m s⁻¹[1]
3. Gamma rays have a much higher frequency, so each photon carries much more energy[1]
4. They are ionising — able to remove electrons from atoms, which can damage or mutate cellsthe word "ionising" is what the mark scheme looks for[1]

Order as listed; 3.0 × 10⁸ m s⁻¹; gamma is ionising because of its far higher photon energy

1. Converts MHz to Hz: 96.0 × 10⁶ = 9.60 × 10⁷ Hzthe prefix is where this question is won or lost[1]
2. Rearranges c = fλ to λ = c/f[1]
3. λ = 3.0 × 10⁸ / 9.60 × 10⁷ = 3.1 m[1]

3.1 m

1. Infrared use: remote controls / thermal imaging / heatersany one[1]
2. Infrared danger: skin burns[1]
3. Ultraviolet use: sterilising / security marking / detecting forgeriesany one[1]
4. Ultraviolet danger: skin cancer / eye damage[1]

They are all transverse waves, and they all travel at 3.0 × 10⁸ m s⁻¹ in a vacuum. (Also acceptable: none requires a medium; all carry energy.)

Microwaves pass through the atmosphere with little absorption, so the signal reaches the satellite and returns. Infrared is strongly absorbed by the atmosphere.

1. X-rays pass through soft tissue but are absorbed by the denser bone[1]
2. Producing a shadow image on the detector[1]
3. Gamma rays are ionising and can kill living cells[1]
4. A focused beam destroys the tumour cells[1]
5. But healthy cells would also be damaged or mutated, so exposure elsewhere must be minimised[1]
6. Ultraviolet is ionising enough to kill bacteria[1]
7. So it sterilises surfaces and instruments[1]
8. Staff must wear eye protection / avoid skin exposure, since UV causes eye damage and skin cancer[1]

1. The sound gets quieter and eventually cannot be heard[1]
2. The hammer is still seen to strike, so the bell is still vibratingthis detail is a mark — it rules out the bell simply stopping[1]
3. There are fewer air particles to be compressed and to pass the vibration on[1]
4. Sound requires a medium to travel through[1]
5. It cannot travel through a vacuum[1]

1. Total distance travelled = v × t = 1500 × 0.40 = 600 m[1]
2. Recognises this is the distance down and backthe mark the question exists to test[1]
3. Depth = 600 / 2[1]
4. = 300 m[1]

300 m

1. B is louder than A[1]
2. Because it has a larger amplitude[1]
3. B has a higher pitch than A[1]
4. Because waves closer together means a higher frequency[1]

As the cone moves forward it pushes air particles together, forming a compression. As it moves back the particles spread apart, forming a rarefaction.

The sound reflects from a distant hard surface and travels back to the listener. Because sound travels at a finite speed, the reflected sound arrives later than the direct one.

1. Distance travelled by the first echo = 340 × 0.60 = 204 m[1]
2. Recognises this is there and back[1]
3. Distance to the nearer cliff = 102 m[1]
4. Distance travelled by the second echo = 340 × 1.0 = 340 m[1]
5. Halves it[1]
6. Distance to the further cliff = 170 m[1]
7. Particles in water are much closer together than in air[1]
8. So collisions between them are more frequent[1]
9. And the vibration is passed on more quickly[1]

(a) 102 m (b) 170 m

1. Bring an end of one bar near the middle of the other, or bring the two ends together and reverse oneany workable procedure[1]
2. If repulsion is observed at any point, that bar is the magnet[1]
3. A magnet attracts any magnetic material, magnetised or not[1]
4. So attraction does not distinguish the two; only repulsion does[1]

1. The bar contains domains, small regions that are already magnetic[1]
2. Initially the domains point in random directions and their effects cancel[1]
3. Stroking aligns the domains so they point the same way, and their effects add[1]
4. Heating makes the domains vibrate and return to random directions, so the magnetism is lost[1]

1. The north-seeking pole of a compass points toward geographic north[1]
2. Unlike poles attract, so the pole attracting a north pole must itself be a south pole[1]

A magnet attracts any magnetic material, whether or not it is magnetised, so attraction proves nothing. Only another magnet can be repelled, so repulsion is conclusive.

The bar contains domains that are individually magnetic. When they point in random directions their effects cancel and the bar shows no magnetism; when they are aligned, the effects add and the bar is a magnet.

Soft iron magnetises and demagnetises easily, so the electromagnet loses its magnetism the moment the current stops. Steel would retain it and the device could not be switched off.

1. Beyond the north pole: away from the magnetfield lines leave the north pole[1]
2. At the side: roughly parallel to the magnet, pointing from N toward Sthe compass lies along the field line[1]
3. Beyond the south pole: toward the magnet, because field lines re-enter at the south pole[1]

Away from N, along the side N→S, and back toward S — the compass always lies along the field line.

The rate of flow of electric charge, I = Q/t. Its unit is the ampere (A), where one ampere is one coulomb per second.

The current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature stays constant.

The metal ions vibrate more strongly, so the moving electrons collide with them more often. Each collision impedes the flow, so the resistance rises.

1. Converts the area: 0.50 mm² = 0.50 × 10⁻⁶ m²the step most often dropped[1]
2. Uses ρ = RA/L[1]
3. ρ = (0.068 × 0.50 × 10⁻⁶) / 2.0[1]
4. ρ = 1.7 × 10⁻⁸ Ω mcopper[1]
5. Doubling the length doubles the resistance: 0.136 Ω[1]

ρ = 1.7 × 10⁻⁸ Ω m; R = 0.14 Ω

1. The graph passes through the origin[1]
2. It is a straight line at low potential difference[1]
3. It then curves towards the V axis, so the gradient falls[1]
4. A larger current heats the filament[1]
5. The ions vibrate more and the electrons collide with them more often[1]
6. So the resistance increases and the current no longer rises in proportion[1]
7. R = V/I = 6.0 / 0.50 = 12 Ω[1]
8. P = VI = 6.0 × 0.50 = 3.0 W[1]

(c) 12 Ω and 3.0 W

1. Total resistance = 20 + 25 = 45 Ω[1]
2. Uses I = V/R[1]
3. I = 9.0 / 45 = 0.20 A[1]
4. Uses V = IR for the thermistor[1]
5. V = 0.20 × 25 = 5.0 V[1]
6. The potential difference across the thermistor decreases[1]
7. Its resistance falls as it warms, so it takes a smaller share of the supply voltage[1]

(a) 0.20 A (b) 5.0 V (c) it falls

1. 1/R = 1/8.0 + 1/8.0 = 0.25, so R = 4.0 Ωone mark for the method, one for inverting correctly[2]
2. Total = 3.0 + 4.0 = 7.0 Ω[1]
3. I = V/R = 9.0 / 7.0 = 1.3 Aaccept 1.29[1]
4. Uses V = IR for the 3.0 Ω resistor[1]
5. V = 1.29 × 3.0 = 3.9 V[1]

(a) 4.0 Ω (b) 7.0 Ω (c) 1.3 A (d) 3.9 V

1. Its resistance decreases[1]
2. The thermistor now takes a smaller share of the supply voltage[1]
3. So a larger share appears across the fixed resistor[1]
4. The output voltage therefore increases[1]

1. Each lamp receives the full mains voltage[1]
2. So each operates at its correct brightness[1]
3. If one lamp fails, the circuit through the others is unbroken[1]
4. So the rest continue to work, and each can be switched independently[1]

1. The total resistance halves[1]
2. Because the second branch gives the current an additional path, so more current flows for the same potential difference[1]

It halves. The second branch gives the current an additional path, so more current flows for the same potential difference.

1. There is only one path for the charge to follow[1]
2. So the same charge passes through each component every second[1]

There is only one path for the charge to follow, so the same charge passes through each component every second.

1. Uses 1/R = 1/R₁ + 1/R₂[1]
2. 1/R = 1/4.0 + 1/12 = 0.25 + 0.0833 = 0.3333[1]
3. R = 3.0 Ωinverting is a separate mark[1]
4. Total resistance = 6.0 + 3.0 = 9.0 Ω[1]
5. Uses I = V/R[1]
6. I = 12 / 9.0 = 1.33 A[1]
7. P.d. across the parallel section = 1.33 × 3.0 = 4.0 Vboth branches share this[1]
8. Uses I = V/R for the 12 Ω branch[1]
9. I = 4.0 / 12 = 0.33 A[1]

(a) 3.0 Ω (b) 1.33 A (c) 0.33 A

1. Uses I = P/V = 2300 / 230converting kW to W[1]
2. I = 10 A[1]
3. 13 A fuse[1]
4. It is the next standard rating above the normal working current of 10 A — a 5 A fuse would blow in normal usethe justification is a separate mark[1]
5. Energy = 2.3 kW × 0.25 h = 0.575 kWh15 minutes is 0.25 hours[1]
6. Cost = 0.575 × 25 = 14.4 rupees[1]

(a) 10 A (b) 13 A, the next rating above 10 A (c) about 14 rupees per day

1. Green and yellow[1]
2. Connected to the metal case[1]
3. A fault would send a very large current from the live wire through the case to earth[1]
4. This large current melts the fuse[1]
5. Which disconnects the live supply, so the case cannot give a shockthe fuse must be in the live wire for this to work[1]

1. Converts to kilowatts: 60 W = 0.060 kW[1]
2. E = 0.060 × 8.0 = 0.48 kWh[1]
3. Converts hours to seconds: 8.0 × 3600 = 28 800 s[1]
4. E = 60 × 28 800 = 1.73 × 10⁶ J[1]

0.48 kWh, or 1.7 × 10⁶ J

When the fuse blows it must disconnect the appliance from the dangerous side of the supply. A fuse in the neutral would leave the appliance connected to the live wire and still dangerous.

The energy transferred by an appliance of power 1 kilowatt operating for 1 hour. It is a unit of energy, not power.

1. Uses E = Pt with power in kW and time in hours[1]
2. E = 3.0 × 2.5 = 7.5 kWh[1]
3. Total lamp power = 5 × 12 = 60 W = 0.060 kW[1]
4. Uses E = 0.060 × 6.0[1]
5. = 0.36 kWh[1]
6. Total = 7.5 + 0.36 = 7.86 kWh[1]
7. Cost = 7.86 × 22 = 173 rupees[1]
8. I = P/V = 3000 / 230 = 13.0 A[1]
9. A 13 A fuse is marginal — a higher-rated fuse or a dedicated circuit is neededaccept 13 A with a comment, or a stated higher rating[1]

(a) 7.5 kWh (b) 0.36 kWh (c) about 173 rupees (d) 13 A

1. Uses V_s/V_p = N_s/N_p[1]
2. V_s = 230 × 5000/200[1]
3. V_s = 5750 V[1]
4. Step-upmore turns on the secondary[1]
5. Direct current produces a constant magnetic field in the core[1]
6. A changing field is required to induce an e.m.f., so nothing is induced in the secondarythe word "changing" is the mark[1]

(a) 5750 V (b) step-up (c) d.c. gives a constant field, and induction needs a changing one

1. The needle deflects to one side while the magnet is moving[1]
2. Move the magnet faster[1]
3. Use a stronger magnet, or a coil with more turnsany second valid change[1]
4. The needle returns to zero — no deflection[1]
5. There is no change in the magnetic field through the coil, and induction requires a change[1]

1. For a given power, a higher voltage means a smaller currentfrom P = VI[1]
2. Power lost as heat in the cables is I²R, so a smaller current wastes much less energythe I² is the key point[1]
3. A step-up transformer raises the voltage at the power station[1]
4. A step-down transformer lowers it again for safe use in homes[1]

Increase the current through the coil, or use a stronger magnetic field. (Also acceptable: increase the number of turns on the coil.)

Soft iron is easily magnetised and demagnetised, so it follows the rapidly alternating field of the primary and carries the changing flux efficiently to the secondary.

1. Uses I = P/V = 20 × 10⁶ / 25 × 10³[1]
2. I = 800 A[1]
3. Uses P = I²R = 800² × 4.0[1]
4. = 2.56 × 10⁶ W = 2.56 MWnearly 13% of the output[1]
5. New current = 20 × 10⁶ / 400 × 10³ = 50 A[1]
6. New loss = 50² × 4.0[1]
7. = 1.0 × 10⁴ W = 10 kW[1]
8. A reduction by a factor of 256, because the current fell by 16 and the loss depends on I²the point of the question[1]
9. Turns ratio N_s : N_p = 400 : 25 = 16 : 1[1]

(a) 800 A (b) 2.56 MW (c) 50 A and 10 kW (d) 16 : 1

1. T = 6.0 × 2.0 ms = 12 ms[1]
2. = 0.012 sconversion needed before finding f[1]
3. Uses f = 1/T[1]
4. f = 83 Hzaccept 83.3[1]
5. Amplitude = 2.5 × 4.0 = 10 Vcentre to peak[1]
6. Peak-to-peak = 20 Vtwice the amplitude[1]

T = 0.012 s, f = 83 Hz, amplitude 10 V, peak-to-peak 20 V

1. B has twice the frequency of A[1]
2. Because the period is halved, and f = 1/T[1]
3. B is louder than A[1]
4. Because its amplitude is twice as large[1]

1. D.C. gives a straight horizontal linedisplaced from the centre by an amount showing the voltage[1]
2. A.C. gives a repeating wave[1]
3. Because d.c. has a constant voltage while a.c. reverses direction and varies continuously with time[1]

The time-base sets the time represented by each horizontal division. The Y-gain sets the voltage represented by each vertical division.

D.C. gives a straight horizontal line displaced from the centre. A.C. gives a repeating wave that rises the same distance above and below the centre line.

1. T = 8.0 × 0.50 ms = 4.0 ms[1]
2. = 4.0 × 10⁻³ s[1]
3. Uses f = 1/T[1]
4. f = 250 Hz[1]
5. Amplitude = 3.5 × 0.20 = 0.70 V[1]
6. Peak-to-peak = 1.4 V[1]
7. Twice as many complete waves appear across the screeneach cycle now takes 4 divisions[1]
8. The height of the trace is unchanged, since the voltage has not alteredthe mark most often missed[1]

(a) 4.0 ms (b) 250 Hz (c) 0.70 V and 1.4 V (d) twice as many waves, same height

1. 92 protonsthe proton number[1]
2. 235 − 92 = 143 neutrons[1]
3. 92 electrons, since the atom is neutral[1]
4. Same number of protons (92); different number of neutrons (146 instead of 143)[1]
5. Chemical behaviour depends on the electrons[1]
6. Both have 92 electrons arranged identically, so they react in the same way[1]

(a) 92 p, 143 n, 92 e (b) same Z, different A (c) identical electron arrangement

1. Most alpha particles passed straight through[1]
2. So the atom is mostly empty space[1]
3. Some were deflected through large angles[1]
4. So there is a concentrated positive charge repelling them[1]
5. A very few were reflected almost straight back[1]
6. So the nucleus is very small and contains most of the atom's mass[1]

1. In that model the positive charge is spread thinly throughout the atom[1]
2. So the repulsive force on an alpha particle anywhere would be small[1]
3. It could not produce the large-angle deflections or backscattering that were observed[1]

The nucleon number A is the total number of protons and neutrons in the nucleus. The proton number Z is the number of protons alone.

They have the same number of protons and therefore the same number of electrons in the same arrangement. Chemical behaviour is decided by the electrons, not by the number of neutrons.

1. Almost all the alpha particles passed straight through[1]
2. A very small fraction were deflected through large angles, some straight back[1]
3. Passing straight through shows the atom is mostly empty space[1]
4. Large deflections show a concentrated region of positive charge[1]
5. Which repels the positive alpha particle[1]
6. Backward scattering shows that region is also very massive, and very small[1]
7. So each alpha particle meets at most one nucleus[1]
8. A thicker foil would cause multiple scattering and the result could not be interpreted[1]

1. 18 hours is 3 half-lives18 ÷ 6[1]
2. Halves three times: 800 → 400 → 200 → 100[1]
3. 100 counts per minute[1]
4. Each half-life removes only half of what remains, so some always remains[1]
5. Temperature or pressure[1]
6. Chemical state or physical form of the sampleany second valid factor[1]

(a) 100 counts/min (b) halving never reaches zero (c) temperature, pressure, chemical state

1. Alpha: A = 218 − 4 = 214[1]
2. Z = 84 − 2 = 82lead[1]
3. Beta: A unchanged at 214[1]
4. Z = 82 + 1 = 83bismuth[1]
5. A neutron changes into a proton and an electron, and the electron is emitted[1]

(a) ²¹⁴₈₂Pb (b) ²¹⁴₈₃ (c) a neutron becomes a proton plus an emitted electron

1. Gamma[1]
2. It is penetrating enough to leave the body and be detected, and least ionising so it does least damageboth halves wanted[1]
3. Short, so the activity falls quickly and the patient is not exposed for long[1]
4. But not so short that it decays away before the scan can be completedthe balance is the point of the question[1]

Handle it with long tongs to increase the distance from the body, and return it to its lead-lined container immediately after use. (Also acceptable: never point it at anyone; minimise exposure time.)

The low level of ionising radiation always present in the environment. Sources include radon gas from rocks, cosmic rays, medical X-rays and food.

1. The time taken for the number of undecayed nuclei in the sample to halve[1]
2. Equivalently, the time for the count rate to fall to half its value; the process is random so this is an average[1]
3. 32 days is 4 half-lives[1]
4. Uses 640 ÷ 2⁴[1]
5. = 40 counts per minute[1]
6. The extra 15 counts per minute is background radiation[1]
7. It is measured with the source removed and subtracted from every reading[1]
8. The proton number increases by 1[1]
9. The nucleon number is unchangeda neutron becomes a proton plus an electron[1]

(b) 40 counts per minute

1. The Earth's rotation on its axis, once every 24 hours[1]
2. The tilt of the Earth's axis, about 23.5°[1]
3. A hemisphere tilted toward the Sun receives light at a steeper angle, concentrated over a smaller area[1]
4. And has more hours of daylight, so it is warmer[1]
5. The distance varies by only a few per cent[1]
6. And the Earth is actually closest to the Sun during the northern winter, which is the opposite of what that explanation would predictthe decisive point[1]

(a) rotation (b) axial tilt, giving steeper light and longer days (c) distance varies little and in the wrong direction

1. Converts the period to seconds: 27.3 × 24 × 3600 = 2.36 × 10⁶ sdays → hours → seconds[1]
2. Uses v = 2πr/T[1]
3. v = 2π × 3.8 × 10⁸ / 2.36 × 10⁶[1]
4. v = 1.0 × 10³ m s⁻¹about 1 km/s[1]

1.0 × 10³ m s⁻¹

1. A planet's orbit is nearly circular; a comet's is highly elliptical[1]
2. A comet's distance from the Sun therefore varies enormously[1]
3. Gravitational attraction is much stronger when it is close to the Sun[1]
4. So it moves fastest at its closest approach and slowest when far away[1]

A planet follows a nearly circular orbit and stays at a roughly constant distance from the Sun. A comet follows a highly elliptical orbit, so its distance and speed change greatly.

The astronaut and the spacecraft are both falling freely towards the Earth with the same acceleration. There is no contact force between them, so the astronaut feels no weight.

1. The direction of motion is continually changing[1]
2. So the velocity is changing, because velocity is a vector[1]
3. A changing velocity is an acceleration[1]
4. The resultant force acts towards the centre of the orbit[1]
5. It is the gravitational attraction of the Earth[1]
6. Gravitational field strength is greater closer to the Earth[1]
7. So a larger centripetal force is needed to hold the satellite in that orbit[1]
8. Which requires a greater orbital speed, so the period is shorter[1]

1. Nuclear fusionnot burning[1]
2. Hydrogen nuclei fuse to form helium[1]
3. It expands to become a red giant[1]
4. Then throws off its outer layers as a planetary nebula, leaving a white dwarf[1]
5. A much more massive star becomes a red supergiant and explodes as a supernova[1]
6. Leaving a neutron star or a black hole[1]

Fusion of hydrogen to helium; red giant → planetary nebula → white dwarf; massive stars instead go supergiant → supernova → neutron star or black hole

1. They are moving away from us[1]
2. The further away a galaxy is, the greater its redshift — so the faster it is receding[1]
3. This shows the Universe is expanding[1]
4. So in the past everything was closer together, in a hot dense state[1]
5. The cosmic microwave background radiation[1]

Receding; further means greater redshift; therefore expansion, therefore a hot dense origin; plus the CMB

1. A more massive star has a much stronger inward gravitational force[1]
2. So the core is hotter and denser, and fusion proceeds much faster[1]
3. It therefore uses up its hydrogen far more quickly than the extra supply lasts[1]

Nuclear fusion in the core, in which hydrogen nuclei join to form helium and release energy.

The light from distant galaxies is shifted towards longer wavelengths, which shows they are moving away from us. The further away a galaxy is, the greater its red-shift and so the faster it recedes.

1. Gravity pulls the material of the star inwards[1]
2. The outward pressure from the energy released by fusion pushes outwards[1]
3. The two are balanced, so the star neither collapses nor expands[1]
4. The core contracts and the outer layers expand and cool[1]
5. The Sun becomes a red giant[1]
6. It then sheds its outer layers and the core remains as a white dwarf[1]
7. Light from almost every distant galaxy is red-shifted, so they are all moving away[1]
8. The more distant the galaxy the greater the red-shift, so the universe is expanding[1]
9. Running that expansion backwards means everything began from a single point[1]