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Saxony Abitur Physics study materials
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Saxony Abitur Physics practice questions

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Question 1Electricity Magnetism

Velocity filter: charged particle undeflected in perpendicular E and B when:

  1. v = E/B Correct answer.
  2. v = B/E
  3. v = EB
  4. v = E²/B

Explanation

For an undeflected particle the electric and magnetic forces balance: qE = qvB, so the selected speed is v = E/B.

Question 2Electricity Magnetism

Standard thin-strip Hall voltage formula is:

  1. U_H = IB/(n e d) Correct answer.
  2. U_H = n e B / I
  3. U_H = I B d /(n e)
  4. U_H = n e I /(B d)

Explanation

U_H = IB/(n e d) for the usual strip geometry (d = thickness along B).

Question 3Electricity Magnetism

Electric field lines between oppositely charged parallel plates (ideal, away from edges):

  1. Uniform, straight, and perpendicular to the plates Correct answer.
  2. Closed circles around each plate
  3. Start on the negative plate and end on the positive
  4. Empty in the middle, dense only at the edges

Explanation

Ideal parallel-plate E is uniform and perpendicular, from + to −. Fringing exists near edges.

Question 4Electricity Magnetism

In Millikan's experiment, an oil drop of mass m and charge q = −Ne is held motionless. If E points vertically downward, the balance condition is:

  1. Ne E = mg Correct answer.
  2. Ne E = 2 mg
  3. E = mg
  4. N = mg E

Explanation

Electric force on negative charge in downward E is upward (F = qE with q < 0). Magnitude: Ne E = mg for hovering.

Question 5Electricity Magnetism

Two point charges of equal magnitude and opposite sign form an electric dipole. On the perpendicular bisector far from the dipole, E is approximately:

  1. Parallel to the dipole axis (antiparallel to p) and falls as 1/r³ Correct answer.
  2. Radial like a point charge (~1/r²)
  3. Zero everywhere on the bisector
  4. Parallel to p and falls as 1/r²

Explanation

On the equatorial line, E is antiparallel to p and |E| ∝ 1/r³ for r ≫ dipole size.

Question 6Waves Optics

Standing wave on a string fixed at both ends: length 1.20 m, 3 antinodes (3rd harmonic). Wavelength?

  1. 0.80 m Correct answer.
  2. 1.20 m
  3. 0.40 m
  4. 2.40 m

Explanation

For n = 3: L = 3λ/2 ⇒ λ = 2L/3 = 2.40/3 = 0.80 m.

Question 7Waves Optics

Double-slit: d = 0.20 mm, screen at L = 1.5 m, bright fringe spacing Δy = 3.0 mm. Wavelength?

  1. 400 nm Correct answer.
  2. 500 nm
  3. 600 nm
  4. 300 nm

Explanation

Δy = λL/d ⇒ λ = Δy d / L = (3.0×10⁻³)(0.20×10⁻³)/1.5 = 6.0×10⁻⁷/1.5 = 4.0×10⁻⁷ m = 400 nm.

Question 8Waves Optics

LC circuit: L = 2.0 mH, C = 8.0 μF. Thomson period T = 2π√(LC) ≈

  1. 0.79 ms Correct answer.
  2. 0.25 ms
  3. 5.0 ms
  4. 0.13 ms

Explanation

√(LC) = √(2.0×10⁻³×8.0×10⁻⁶) = √(1.6×10⁻⁸) = 1.265×10⁻⁴; T = 2π×1.265×10⁻⁴ ≈ 7.9×10⁻⁴ s ≈ 0.79 ms.

Question 9Waves Optics

Resonance in a driven damped oscillator occurs when the driving frequency is near:

  1. The natural frequency of the undamped system (for light damping) Correct answer.
  2. Zero frequency only
  3. Infinity
  4. Twice the natural frequency exactly, always

Explanation

For light damping, amplitude resonance is near ω₀ = √(k/m). Power resonance is at ω₀.

Question 10Waves Optics

A guitar string of length 0.65 m has fundamental frequency 330 Hz. Wave speed on the string?

  1. 429 m/s Correct answer.
  2. 215 m/s
  3. 330 m/s
  4. 650 m/s

Explanation

For fundamental, λ = 2L = 1.30 m; v = fλ = 330×1.30 = 429 m/s.

Question 11Waves Optics

Single-slit diffraction: first minimum at angle θ satisfies:

  1. a sinθ = λ Correct answer.
  2. a sinθ = λ/2
  3. a sinθ = 3λ/2 for first minimum
  4. a = λ sinθ

Explanation

For single-slit, minima at a sinθ = mλ (m = ±1, ±2, …). First minimum: a sinθ = λ.

Question 12Waves Optics

In an electromagnetic wave, E and B fields are:

  1. Perpendicular to each other and to the propagation direction Correct answer.
  2. Parallel to each other
  3. Only E oscillates; B is static
  4. Longitudinal oscillations along the ray

Explanation

EM waves are transverse: E ⊥ B ⊥ propagation, with |E|/|B| = c in vacuum.

Question 13Waves Optics

Doppler effect: source of 680 Hz sound moves toward a stationary observer at 20 m/s (v_sound = 340 m/s). Observed frequency ≈

  1. 723 Hz Correct answer.
  2. 640 Hz
  3. 680 Hz
  4. 700 Hz

Explanation

f' = f × v/(v−v_s) = 680×340/(340−20) = 680×340/320 = 680×1.0625 ≈ 722.5 Hz ≈ 723 Hz.

Question 14Modern Physics

An electron accelerated through 150 V has de Broglie wavelength about: (use λ = h/√(2m e U), ≈ 1.50/√U nm with U in volts for electrons)

  1. 0.10 nm Correct answer.
  2. 0.15 nm
  3. 1.0 nm
  4. 0.010 nm

Explanation

λ(nm) ≈ 1.226/√U ≈ 1.226/√150 ≈ 1.226/12.25 ≈ 0.100 nm. (Common exam approximation ~1.5/√U also gives ~0.12 nm; closest listed is 0.10 nm.)

Question 15Modern Physics

Photon emitted in the hydrogen transition n = 3 → n = 2 (Balmer). Photon energy?

  1. 1.89 eV Correct answer.
  2. 10.2 eV
  3. 12.1 eV
  4. 3.40 eV

Explanation

ΔE = E₃−E₂ wait: emitted photon E = E_upper−E_lower magnitudes: E = −13.6(1/9 − 1/4) = −13.6(0.111−0.250) = −13.6(−0.139) = 1.89 eV.

Question 16Modern Physics

Relationship between decay constant λ and half-life T½:

  1. λ = ln2 / T½ Correct answer.
  2. λ = T½ / ln2
  3. λ = 1/T½
  4. λ = ln2 × T½

Explanation

N = N₀ e^(−λt); at t = T½, 1/2 = e^(−λ T½) ⇒ λ = ln2 / T½.

Question 17Modern Physics

Beta-minus decay: a nucleus emits an electron and an antineutrino. Z changes by:

  1. +1 Correct answer.
  2. −1
  3. −2
  4. 0

Explanation

n → p + e⁻ + ν̄_e inside the nucleus ⇒ Z increases by 1; A unchanged.

Question 18Modern Physics

A photon of energy 2.0 MeV creates an electron–positron pair in matter. Kinetic energy shared by the pair (total) is about: (2 m_e c² ≈ 1.022 MeV)

  1. 0.98 MeV Correct answer.
  2. 2.0 MeV
  3. 1.022 MeV
  4. 3.0 MeV

Explanation

Threshold is 1.022 MeV; leftover K = 2.0 − 1.022 ≈ 0.98 MeV shared by e⁻ and e⁺.

Question 19Modern Physics

Planck's relation E = hf implies that for fixed intensity, higher-frequency light means:

  1. Each photon carries more energy; fewer photons per second may still deliver the same power Correct answer.
  2. Photons become slower than c
  3. Intensity must increase with frequency
  4. Wavelength must increase

Explanation

Power = (energy per photon)×(photon rate). Higher f ⇒ larger hf; same intensity can mean fewer photons/s.

Question 20Mechanics

A stone is thrown vertically upward at 15 m/s. Taking g = 9.81 m/s² and neglecting air resistance, how high does it rise?

  1. 11.5 m Correct answer.
  2. 15.0 m
  3. 22.9 m
  4. 7.65 m

Explanation

At the top v = 0. From v² = v₀² − 2gh: h = v₀²/(2g) = 225/19.62 ≈ 11.5 m.

Question 21Experimental Reasoning

In a GCE A-Level physics practical, a student records the diameter of a wire as 0.52 mm using a micrometer screw gauge with a zero error of +0.03 mm. What is the corrected diameter?

  1. 0.52 mm
  2. 0.58 mm
  3. 0.49 mm Correct answer.
  4. 0.55 mm

Explanation

A positive zero error means the instrument reads a value when the jaws are closed, so the error must be subtracted from every reading. Here 0.52 − 0.03 = 0.49 mm. Adding the error would double-count the fault rather than remove it.

Question 22Experimental Reasoning

A digital stopwatch displays elapsed time in increments of 0.01 s, for example 12.33 s,12.34 s and 12.35 s. What is the resolution of this displayed time?

  1. 12.34 s
  2. 0 s
  3. 0.005 s
  4. 0.01 s Correct answer.

Explanation

The smallest stated difference between adjacent displayed times is 0.01 s, so the display resolution is 0.01 s. This does not establish the uncertainty of a manually timed event: reaction time, instrument behavior and the measurement method can contribute additional uncertainty.

Question 23Experimental Reasoning

A metre rule is used to measure the length of a pendulum. Which practice best reduces the uncertainty in this length measurement?

  1. Align the rule with the measured length, view the relevant graduation with the line of sight perpendicular to the scale, and use a clear reference mark Correct answer.
  2. Measure the length only once to avoid confusion
  3. Hold the rule at an angle to the string for a firmer grip
  4. Round the reading to the nearest centimetre

Explanation

Aligning the rule with the measured length avoids an oblique length comparison. Viewing the graduation perpendicularly reduces parallax caused by separation between the indicator and scale. Use clear reference marks and measure the pendulum length from its pivot to the bob center. Resolution and repeatability still limit the result.

Question 24Experimental Reasoning

In an experiment to verify Ohm's law, a student plots a graph of current I against potential difference V. What does the gradient of this graph represent?

  1. The reciprocal of the resistance Correct answer.
  2. The resistance of the resistor
  3. The power dissipated
  4. The charge passed per second

Explanation

Ohm's law gives I = V/R, so plotting I on the vertical axis against V gives a straight line through the origin with gradient 1/R. The resistance itself would be the gradient only if V were plotted against I.

Question 25Experimental Reasoning

A student takes six readings of the time for 20 oscillations of a simple pendulum. Which quantity is the most appropriate to report as the period?

  1. The mean of the six times divided by 20 Correct answer.
  2. The mean of the six times multiplied by 20
  3. The difference between the largest and smallest times
  4. The largest of the six times divided by 20

Explanation

The period is the time for one oscillation, so the mean time for 20 oscillations is divided by 20. Averaging repeated timings reduces the effect of random reaction-time errors.

Question 26Experimental Reasoning

Which instrument is most suitable for measuring the internal diameter of a narrow glass tube?

  1. Metre rule
  2. Vernier calipers Correct answer.
  3. Micrometer screw gauge
  4. Travelling microscope

Explanation

Vernier calipers have internal jaws that can be inserted into a bore to measure internal diameter. A micrometer screw gauge is designed for external dimensions of thin objects and has no internal jaws.

Question 27Experimental Reasoning

A student measures the mass of a block five times and obtains values that agree closely with one another, but the accepted value is 20% higher. Which description fits these results?

  1. Accurate but not precise
  2. Neither accurate nor precise
  3. Both accurate and precise
  4. Precise but not accurate Correct answer.

Explanation

Precision describes how closely repeated readings agree with each other, while accuracy describes closeness to the true value. Consistent readings that all differ from the accepted value by the same amount indicate a systematic error, so the results are precise but inaccurate.

Question 28Experimental Reasoning

In a practical on the refraction of light through a glass block, which set of apparatus is essential for measuring the angles of incidence and refraction?

  1. Ammeter, voltmeter and rheostat
  2. Ray box, protractor and plain paper Correct answer.
  3. Stopwatch, metre rule and retort stand
  4. Thermometer, beaker and balance

Explanation

Angles are found by tracing the incident and refracted rays on paper and measuring them with a protractor, with a ray box providing a narrow beam. The other sets belong to timing, thermal and electrical experiments.

Question 29Experimental Reasoning

A spring's loading graph deviates from its initial straight line. Which additional observation most directly indicates permanent deformation? Assume the temperature is unchanged, the load is fully removed, the spring has settled, and the length measurements are checked.

  1. The loading graph alone is nonlinear, with no observation after unloading
  2. The unloaded spring remains longer than its original unloaded length Correct answer.
  3. The load axis is relabelled from newtons to kilonewtons
  4. The extension is reported in metres instead of centimetres

Explanation

A residual increase in the checked unloaded length under the stated conditions indicates permanent deformation. A departure from a straight loading graph establishes a failure of the initial linear relation, but does not by itself prove irreversible change. The limit of proportionality and the limit of elastic recovery are different concepts.

Question 30Experimental Reasoning

In an experiment to determine the specific heat capacity of a metal block, which improvement most directly reduces the largest systematic error?

  1. Insulating the block to reduce heat loss to the surroundings Correct answer.
  2. Increasing the mass of the block
  3. Using a thermometer with a finer scale
  4. Repeating the heating and averaging

Explanation

The main systematic error is energy lost from the block to the air, which makes the calculated specific heat capacity too high. Insulation reduces this loss; a finer thermometer or repeats address random reading errors, which are usually smaller.

Question 31Experimental Reasoning

A student measures the resistance of a wire using an ammeter and voltmeter and obtains R = 4.0 Ω. If the voltmeter reading is 2.0 V with an uncertainty of ±0.1 V and the ammeter reading is 0.50 A with an uncertainty of ±0.02 A, what is the percentage uncertainty in R?

  1. 9% Correct answer.
  2. 5%
  3. 2%
  4. 4%

Explanation

For a quotient, percentage uncertainties add: 0.1/2.0 gives 5% and 0.02/0.50 gives 4%, so the total is 9%. The absolute uncertainty in R is then 0.09 × 4.0 = 0.36 Ω.

Question 32Experimental Reasoning

In a Young's double-slit experiment, a student measures the fringe separation by counting across many fringes rather than measuring one fringe. Why is this done?

  1. It increases the wavelength of the light used
  2. It eliminates the effect of the screen distance
  3. It removes the need to measure the slit separation
  4. It reduces the percentage uncertainty in the fringe separation Correct answer.

Explanation

Measuring across, say, ten fringes and dividing gives a larger length, so the fixed reading uncertainty becomes a smaller fraction of the measured value. It does not change the physics of the interference pattern.

Question 33Experimental Reasoning

A student plots a graph of the square of the period T² against the length l of a simple pendulum. What does the gradient of this graph equal?

  1. g/4π²
  2. 2π/g
  3. 4π²/g Correct answer.
  4. g/2π

Explanation

From T = 2π√(l/g), squaring gives T² = (4π²/g)l, so a plot of T² against l is a straight line through the origin with gradient 4π²/g. Rearranging this gradient gives g.

Question 34Experimental Reasoning

When reading a burette or a thermometer, a student consistently views the meniscus from above. What type of error does this introduce and how is it corrected?

  1. A calibration error, corrected by using a different instrument
  2. A random error, corrected by taking more readings
  3. A zero error, corrected by subtracting a constant
  4. A systematic parallax error, corrected by aligning the eye with the meniscus Correct answer.

Explanation

Viewing from a fixed wrong angle shifts every reading in the same direction, so the error is systematic. The remedy is to place the eye level with the meniscus so the line of sight is perpendicular to the scale.

Question 35Experimental Reasoning

A student investigating the I–V characteristic of a filament lamp finds that the graph curves so that the gradient decreases as V increases. What conclusion follows?

  1. The lamp obeys Ohm's law at all voltages
  2. The filament has a constant resistance
  3. The resistance of the filament increases as its temperature rises Correct answer.
  4. The current is independent of the potential difference

Explanation

A decreasing gradient on an I–V graph means the ratio V/I rises, so the resistance increases. This happens because the filament heats up and its lattice ions scatter electrons more strongly.

Question 36Experimental Reasoning

In a moment experiment, a metre rule is balanced on a pivot and a known mass is hung at a measured distance. Which precaution most improves the reliability of the result?

  1. Finding the balance point of the rule before adding the masses Correct answer.
  2. Using the heaviest available mass
  3. Reading the distances to the nearest 10 cm
  4. Balancing the rule on a knife edge held by hand

Explanation

The rule's own weight acts at its centre of gravity, so its balance point must be located and allowed for before moments are taken. Holding the pivot by hand allows movement and adds random error.

Question 37Experimental Reasoning

A student measures the diameter of a small ball five times and obtains 2.14, 2.15, 2.13, 2.16 and 2.14 cm. What is the best estimate of the mean diameter with its uncertainty expressed as the range?

  1. 2.144 cm ± 0.005 cm
  2. 2.144 cm ± 0.001 cm
  3. 2.144 cm ± 0.015 cm Correct answer.
  4. 2.144 cm ± 0.03 cm

Explanation

The mean of the five readings is 2.144 cm. The range is 2.16 − 2.13 = 0.03 cm, and the uncertainty is conventionally quoted as half the range, 0.015 cm.

Question 38Experimental Reasoning

In an experiment to determine the density of an irregular solid, a student uses a displacement can. Which procedural detail is most important for an accurate result?

  1. Using a beaker rather than a measuring cylinder
  2. Dropping the solid in quickly from a height
  3. Ensuring the can is filled exactly to the overflow spout before displacement Correct answer.
  4. Wetting the solid before lowering it

Explanation

The can must be filled to the level of the spout so that the volume collected corresponds exactly to the volume of the solid. If it is under-filled, the first displaced water merely raises the level to the spout and the collected volume is too small.

Question 39Experimental Reasoning

A student investigating the cooling of a liquid plots temperature against time and obtains a smooth curve. To test whether the cooling follows an exponential law, what is the best approach?

  1. Plot temperature against the square of time
  2. Plot the logarithm of the excess temperature against time and check for a straight line Correct answer.
  3. Read only the first and last points
  4. Plot temperature against time and check for a straight line

Explanation

Newton's law of cooling gives an exponential decay of excess temperature, so taking logarithms linearises the relationship. A straight-line log plot confirms the exponential form and its gradient gives the cooling constant.

Question 40Experimental Reasoning

In a potentiometer experiment to compare the e.m.f.s of two cells, the balance length for the first cell is 60.0 cm and for the second is 45.0 cm. What is the ratio of the e.m.f. of the first cell to that of the second?

  1. 9:16
  2. 16:9
  3. 4:3 Correct answer.
  4. 3:4

Explanation

At balance the e.m.f. is proportional to the balance length, so the ratio equals 60.0/45.0 = 4/3. The potentiometer draws no current at balance, so the reading equals the e.m.f. rather than the terminal p.d.

Question 41Experimental Reasoning

A student uses a resonance tube to find the speed of sound and obtains first and second resonance lengths of 17.0 cm and 51.5 cm at a fixed frequency. Why is the difference between successive resonance lengths used rather than a single length?

  1. The difference eliminates the tuning fork
  2. The difference gives the wavelength directly in centimetres
  3. The difference doubles the frequency
  4. The difference removes the end correction Correct answer.

Explanation

Each resonance length includes the same end correction, so subtracting successive lengths cancels it. The difference equals half a wavelength, from which the wavelength and then the speed follow.

Question 42Experimental Reasoning

A student determines g using a pendulum and finds T² against l has gradient 4.05 s² m⁻¹ with a percentage uncertainty of 2%. What is the percentage uncertainty in the value of g obtained?

  1. 4%
  2. 1%
  3. 0.5%
  4. 2% Correct answer.

Explanation

Since g = 4π²/gradient, the only measured quantity carrying uncertainty is the gradient, and 4π² is exact. The percentage uncertainty in g therefore equals that in the gradient, 2%.

Question 43Experimental Reasoning

In an experiment to measure the internal resistance of a cell, a student plots terminal potential difference V against current I and obtains a straight line of gradient −2.0 V A⁻¹ and intercept 1.5 V. What are the e.m.f. and internal resistance?

  1. 1.5 V and 2.0 Ω Correct answer.
  2. 1.5 V and 0.5 Ω
  3. 2.0 V and 1.5 Ω
  4. −1.5 V and 2.0 Ω

Explanation

The equation V = E − Ir shows that the intercept on the V axis is the e.m.f. and the magnitude of the gradient is the internal resistance. Hence E = 1.5 V and r = 2.0 Ω.

Question 44Experimental Reasoning

A student measures the focal length of a converging lens by plotting 1/v against 1/u. The graph is a straight line of gradient −1 and intercept 0.05 cm⁻¹. What is the focal length and what does the gradient confirm?

  1. 20 cm, confirming the lens equation with unit gradient Correct answer.
  2. 20 cm, confirming that magnification is constant
  3. 5 cm, confirming that the image is always real
  4. 0.05 cm, confirming the lens is diverging

Explanation

The lens equation rearranges to 1/v = −1/u + 1/f, so the intercept is 1/f and the gradient is −1. An intercept of 0.05 cm⁻¹ gives f = 1/0.05 = 20 cm, and the unit gradient confirms the expected form.

Question 45Experimental Reasoning

Two students measure the same quantity. Student A reports 5.0 ± 0.1 cm and student B reports 5.00 ± 0.05 cm. Which statement is correct?

  1. A's result is more precise because its uncertainty is larger
  2. B's result is more accurate because it has more decimal places
  3. The two results are inconsistent because the uncertainties differ
  4. B's result is more precise and is consistent with A's within their uncertainties Correct answer.

Explanation

A smaller absolute uncertainty means greater precision, so B's result is more precise. The intervals 4.9–5.1 cm and 4.95–5.05 cm overlap, so the two results agree within their stated uncertainties.

Question 46Experimental Reasoning

A student uses a vernier caliper whose main scale is marked in millimetres and whose vernier scale has 10 divisions occupying 9 mm. The main-scale reading is 24 mm and the sixth vernier division coincides with a main-scale mark. What is the length of the object?

  1. 24.6 mm Correct answer.
  2. 24.0 mm
  3. 24.06 mm
  4. 25.4 mm

Explanation

With 10 vernier divisions spanning 9 mm, the least count is 1 mm − 0.9 mm = 0.1 mm, so each coinciding vernier division adds 0.1 mm. The sixth division coinciding therefore adds 0.6 mm to the main-scale reading of 24 mm. The caliper reading is thus 24 + 0.6 = 24.6 mm, quoted to the instrument's resolution of 0.1 mm.

Question 47Experimental Reasoning

In a practical to verify Ohm's law, a student records potential difference V and current I for a fixed resistor and plots V against I. Which statement about the expected graph is correct?

  1. It is a straight line through the origin whose gradient equals the resistance. Correct answer.
  2. It is a curve of decreasing gradient because the resistor heats up.
  3. It is a straight line through the origin whose gradient equals the reciprocal of the resistance.
  4. It is a straight line with a non-zero intercept on the V axis equal to the e.m.f.

Explanation

Ohm's law gives V = IR, so a plot of V (y-axis) against I (x-axis) is linear through the origin with gradient R. The intercept should be zero for a purely resistive component with no e.m.f. of its own. Checking linearity and the zero intercept is exactly how the law is verified experimentally.

Question 48Experimental Reasoning

A student determines the density of a metal cylinder from ρ = m/(πd²h/4), measuring mass m with a balance, diameter d with a micrometer screw gauge and height h with a vernier caliper. The percentage uncertainties are 0.5% in m, 0.4% in d and 1.0% in h. What is the percentage uncertainty in the calculated density?

  1. 1.9%
  2. 1.5%
  3. 0.9%
  4. 2.3% Correct answer.

Explanation

In the formula the diameter is squared, so its percentage uncertainty is doubled: 2 × 0.4% = 0.8%. Percentage uncertainties add for quantities combined by multiplication and division, giving 0.5% + 0.8% + 1.0% = 2.3%.

Question 49Experimental Reasoning

A student plots a calibration graph of thermocouple e.m.f. against temperature and draws the line of best fit. Several plotted points lie slightly above and below the line. What is the correct purpose of drawing the line of best fit rather than joining the points dot-to-dot?

  1. It averages out random scatter so the gradient and intercept are estimated more reliably. Correct answer.
  2. It guarantees that every experimental point lies exactly on the line.
  3. It removes systematic error present in the readings.
  4. It allows the graph to be extrapolated beyond the calibrated range with confidence.

Explanation

Random fluctuations in individual readings scatter points about the true relationship, and a line of best fit balances these deviations to give the most reliable estimate of gradient and intercept. Systematic errors shift all points in the same way, so they are not removed by fitting but must be traced to the apparatus or method. The fit is a statistical smoothing, not a correction for bias.

Question 50Experimental Reasoning

In a practical to measure the acceleration of free fall using a simple pendulum, a student times 20 oscillations with a stopwatch and divides by 20, repeating for several lengths. Which combination of precautions most directly reduces the uncertainty in the value of g obtained?

  1. Use a heavy bob and a long thread, timing 20 oscillations but measuring length only to the top of the thread.
  2. Use a short pendulum and time a single oscillation to avoid counting errors.
  3. Time 20 oscillations from a large amplitude so the motion is easier to observe.
  4. Use a long pendulum, time many oscillations, and measure length to the centre of the bob with a metre rule plus vernier calipers for the bob diameter. Correct answer.

Explanation

Since g depends on l/T², the fractional uncertainty in l and in T both matter, and timing many oscillations reduces the reaction-time uncertainty in T. A long pendulum increases l and lengthens T, improving the fractional precision of both measurements. Measuring to the centre of the bob, accounting for its diameter, removes a systematic error in l.