IB Physics Quiz: Exploring And Designing

20 questions · exam conditions

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Exploring And DesigningQuestion 1 of 20

A student measures the dimensions of a rectangular block to calculate its volume. The measurements are length $L = 50.0 \pm 0.5$ cm, width $W = 10.0 \pm 0.5$ cm, and height $H = 2.0 \pm 0.5$ cm. Which measurement is the largest source of uncertainty in the calculated volume?

The length, L, because it is the largest dimension.

The width, W, because its absolute uncertainty is large.

The height, H, because it has the largest percentage uncertainty.

All three measurements contribute equally to the uncertainty.

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IB Physics Quiz

IB Physics Quiz: Exploring And Designing

Practice Exploring And Designing in IB Physics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Exploring And Designing, giving you a quick way to practice the rules, question types, and explanations that matter most for IB Physics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The length, L, because it is the largest dimension.
The width, W, because its absolute uncertainty is large.
The height, H, because it has the largest percentage uncertainty. (correct answer)
All three measurements contribute equally to the uncertainty.

Explanation: When multiplying quantities, the percentage (or fractional) uncertainties add up. To find the largest source of uncertainty, we must compare the percentage uncertainties of each measurement. % unc(L) = (0.5/50.0) * 100% = 1%. % unc(W) = (0.5/10.0) * 100% = 5%. % unc(H) = (0.5/2.0) * 100% = 25%. The height measurement has the largest percentage uncertainty (25%) and will therefore contribute the most to the uncertainty in the final calculated volume.

Question 2

A student is testing the hypothesis that the kinetic energy ( $E_k$ ) of an object is proportional to the square of its velocity ( $v$ ). They measure $E_k$ and $v$ for an object of constant mass. To confirm the hypothesis using a linear graph, which quantities should they plot on the y-axis and x-axis respectively?

$E_k$ on the y-axis and $v^2$ on the x-axis. (correct answer)
$E_k$ on the y-axis and $v$ on the x-axis.
$\sqrt{E_k}$ on the y-axis and $v^2$ on the x-axis.
$v$ on the y-axis and $E_k$ on the x-axis.

Explanation: The relationship is

E_k = \frac{1}{2}mv^2

. To linearize this equation in the form

y = mx + c

, we can treat

E_k

y

and

v^2

x

. The equation becomes

y = (\frac{1}{2}m)x

. This shows that a graph of

E_k

versus

v^2

will be a straight line passing through the origin with a gradient of

\frac{1}{2}m

Question 3

A student determines the specific latent heat of vaporization of water by measuring the electrical energy supplied to a heater to boil off a certain mass of water. Their calculated value is significantly larger than the accepted value. Which modification to the experimental design would most effectively improve the accuracy?

Using a more precise voltmeter and ammeter to measure the power supplied to the heater.
Placing a lid on the beaker and insulating the sides to reduce heat loss to the surroundings. (correct answer)
Increasing the duration of the experiment to boil off a larger mass of water.
Using distilled water instead of tap water to ensure the sample is pure.

Explanation: A calculated value that is too large means the energy input (

Q=Pt

) used in the calculation

L=Q/m

was greater than the energy that actually went into vaporizing the water. This is due to systematic heat loss to the surroundings. Insulating the apparatus and using a lid are the most effective ways to minimize this heat loss, thus making the measured energy input a more accurate reflection of the energy used for vaporization.

Question 4

A student is designing an experiment to measure the half-life of a radioactive sample. A key part of the procedure is accounting for background radiation. What is the correct procedure for doing this?

Measure the count rate with the source present, then subtract the first reading taken without the source.
Measure the background count rate for a short time and subtract this constant value from all source readings.
Measure the background count rate over a long period before and after the experiment and use the average. (correct answer)
Ignore the background radiation as it is typically negligible compared to the source's activity.

Explanation: Background radiation is random and can fluctuate. To get a reliable average value, it should be measured for a time period comparable to the main experiment's duration. Measuring it before and after and taking an average accounts for any potential slow drifts in background activity. This average background rate is then subtracted from each measurement of the source's count rate to find the corrected activity of the source itself.

Question 5

A student conducts an experiment to measure the specific heat capacity of a metal block by heating it and observing the temperature rise. To ensure the thermal energy supplied is accurately calculated, they use a voltmeter and an ammeter connected to the heater. What is the correct placement of these meters in the circuit?

Both the voltmeter and the ammeter should be connected in series with the heater.
Both the voltmeter and the ammeter should be connected in parallel with the heater.
The ammeter should be in series with the heater, and the voltmeter should be in parallel with the heater. (correct answer)
The ammeter should be in parallel with the heater, and the voltmeter should be in series with the heater.

Explanation: To measure the power

P=IV

delivered to the heater, one must measure the current

I

flowing through it and the potential difference

V

across it. Ammeters measure current and have very low resistance, so they must be connected in series to have the circuit current flow through them. Voltmeters measure potential difference and have very high resistance, so they must be connected in parallel across the component to measure the potential drop without drawing significant current from the main circuit.

Question 6

A student measures the length of an object with a ruler. They repeat the measurement five times and get the following readings: 25.4 cm, 25.5 cm, 25.3 cm, 25.5 cm, 25.4 cm. Later, they discover the ruler had a zero error, with its end at the -0.2 cm mark instead of 0.0 cm. How should the errors in this experiment be described?

There is only random error, as shown by the variation in readings.
There is only systematic error from the ruler's zero offset.
There is neither random nor systematic error as the average is close to the true value.
There are both random errors causing the scatter and a systematic error causing inaccuracy. (correct answer)

Explanation: The variation in the readings (e.g., 25.3, 25.4, 25.5) indicates the presence of random errors, which cause scatter around an average value. The zero error on the ruler, which causes every reading to be consistently off by the same amount (in this case, 0.2 cm too high), is a systematic error. Real experiments almost always contain both types of error.

Question 7

When investigating Hooke's Law, a student plots a graph of applied force versus spring extension. The data points form a clear straight line that is offset from the origin. Which experimental error is the most likely cause for the best-fit line not passing through the origin?

Consistently misreading the millimetre marks on the ruler between the centimetre marks.
Failing to account for the mass of the weight hanger when recording the applied force. (correct answer)
The spring was stretched beyond its elastic limit before the experiment began.
Random fluctuations in reading the exact position of the pointer on the scale.

Explanation: If the mass of the weight hanger is not accounted for, every force value recorded (

F = m_{added}g

) will be systematically lower than the actual force acting on the spring (

F_{actual} = (m_{added} + m_{hanger})g

). This adds a constant offset to the force, shifting the entire graph. For example, when

m_{added}=0

, there is still a force from the hanger, causing an extension. This means the graph will not pass through the (0,0) origin. Random errors (D) cause scatter, and exceeding the elastic limit (C) would make the graph non-linear.

Question 8

In an experiment to verify the ideal gas law, a student measures the pressure $P$ of a fixed mass of gas in a sealed container as its temperature $T$ is increased. A plot of $P$ versus $T$ (in Kelvin) yields a straight line, but it does not pass through the origin, instead showing a positive pressure intercept at $T=0$ K. What is a plausible systematic error in the design that could cause this result?

The thermometer was not in thermal equilibrium with the gas, consistently reading a lower temperature.
There was a small leak in the container, allowing gas to escape as the temperature increased.
The pressure gauge had a zero error, consistently reading a pressure value higher than the actual pressure. (correct answer)
The volume of the container expanded significantly as the temperature increased.

Explanation: The ideal gas law for a fixed mass and volume is

P = (nR/V)T

. This is a direct proportionality, so the graph of

P

T

(in Kelvin) should be a straight line through the origin (0,0). If the pressure gauge has a positive zero error (e.g., reads 0.1 atm when the pressure is zero), then every measurement will be

P_{measured} = P_{actual} + P_{error}

. This would shift the entire graph vertically upwards, resulting in a positive intercept on the pressure axis.

Question 9

A student hypothesizes that the resistance $R$ of a thermistor is related to its absolute temperature $T$ by the equation $R = R_0 e^{B/T}$ , where $R_0$ and $B$ are constants. To obtain a straight-line graph from which the constant $B$ can be determined, which quantities should be plotted?

$R$ on the y-axis and $1/T$ on the x-axis.
$R$ on the y-axis and $T$ on the x-axis.
$\ln(R)$ on the y-axis and $T$ on the x-axis.
$\ln(R)$ on the y-axis and $1/T$ on the x-axis. (correct answer)

Explanation: To linearize the exponential equation

R = R_0 e^{B/T}

, we can take the natural logarithm of both sides:

\ln(R) = \ln(R_0 e^{B/T})

. Using logarithm rules, this becomes

\ln(R) = \ln(R_0) + \ln(e^{B/T})

, which simplifies to

\ln(R) = B(1/T) + \ln(R_0)

. This equation is in the form

y = mx + c

, where

y = \ln(R)

x = 1/T

, the gradient

m = B

, and the y-intercept

c = \ln(R_0)

. Therefore, plotting

\ln(R)

versus

1/T

will yield a straight line with a gradient equal to B.

Question 10

A student investigates the rate of cooling of a liquid in two different containers, A and B. Container A has a dull black surface, and container B has a shiny silver surface. Both contain the same volume of the same liquid at the same initial temperature. The student concludes that the liquid in container A cools faster because dull black surfaces are better emitters of thermal radiation. Why is this conclusion potentially incomplete?

The material of container A might be a better thermal conductor than container B. (correct answer)
The mass of the liquid in each container might not have been precisely equal.
The ambient room temperature could have fluctuated during the experiment.
The shiny silver surface is a better reflector of thermal radiation.

Explanation: While it is true that dull black surfaces are better emitters (and absorbers) of radiation, heat can also be lost through conduction and convection. If container A is made of a material with a much higher thermal conductivity than container B, it would lose heat faster via conduction through its base and sides. This is a confounding variable. The student's conclusion attributes the entire effect to radiation, which may be invalid if conduction is also a significant, uncontrolled factor.

Question 11

A student plots a graph of current $I$ on the y-axis against potential difference $V$ on the x-axis for a metallic conductor at constant temperature. They find the gradient of the resulting straight-line graph. What physical quantity does this gradient represent?

The resistance $R$ of the conductor.
The resistivity $\rho$ of the conductor's material.
The reciprocal of the resistance $1/R$ of the conductor. (correct answer)
The power $P$ dissipated by the conductor.

Explanation: Ohm's Law is given by

V=IR

. The student is plotting a graph of

y=I

against

x=V

. To match the form of a linear equation

y=mx+c

, we rearrange Ohm's Law to make

I

the subject:

I = (1/R)V

. In this form, the gradient

m

corresponds to

1/R

, the reciprocal of the resistance (also known as conductance).

Question 12

A student is designing an experiment to investigate the interference of sound waves using two loudspeakers connected to the same signal generator. To observe a stable interference pattern of maxima and minima, what is the most critical condition that must be met by the two sound sources?

The loudspeakers must be separated by a distance greater than the wavelength of the sound.
The loudspeakers must emit sound of the same amplitude and frequency.
The loudspeakers must be placed in a room with no reflective surfaces to prevent echoes.
The loudspeakers must be coherent, meaning they emit waves with a constant phase difference. (correct answer)

Explanation: While other factors are important for a clear pattern, the fundamental requirement for a stable, observable interference pattern is that the sources must be coherent. Coherence (a constant phase relationship) ensures that the positions of constructive interference (maxima) and destructive interference (minima) do not shift over time. Connecting both speakers to the same signal generator achieves this. Same frequency (B) is necessary for coherence, but coherence is the more precise and encompassing term for the required condition.

Question 13

A student designs an experiment to investigate how the period of a simple pendulum depends on amplitude. The student plans to measure periods for amplitudes of 5°, 15°, 30°, 45°, and 60°. Which modification would most improve the experimental design?

Include additional amplitude measurements at 2°, 8°, and 12° to better resolve the small-amplitude region where theory predicts linear behavior (correct answer)
Extend the amplitude range to include 75° and 90° to test the pendulum behavior at extremely large displacements
Reduce the number of amplitude values to 15°, 30°, and 45° to allow more time for repeated measurements at each amplitude
Replace the amplitude measurements with different pendulum lengths while keeping amplitude constant at 15° throughout the experiment

Explanation: The simple harmonic motion approximation (

T = 2\pi\sqrt{L/g}

) is most accurate for small amplitudes (typically <15°). To investigate how period depends on amplitude, the student needs data points in the small-amplitude region where the approximation should hold, and larger amplitudes where deviations appear. Choice A provides better resolution where the transition occurs. Choice B tests extreme cases but loses focus on the theoretically important small-amplitude region. Choice C reduces data density. Choice D changes the research question entirely.

Question 14

A student wants to investigate the relationship between the angle of incidence and the angle of refraction when light passes from air into glass. Which combination of variables and controls would provide the most reliable data for determining Snell's law?

Measure multiple angles of incidence with the same wavelength of light, keeping the glass thickness and surface quality constant (correct answer)
Measure one angle of incidence with different wavelengths of light, keeping the glass type and surface quality constant
Measure multiple angles of incidence with different glass types, keeping the wavelength and surface quality constant
Measure multiple angles of incidence with the same glass type, varying the thickness and surface quality systematically

Explanation: To determine Snell's law (

n_1 \sin \theta_1 = n_2 \sin \theta_2

), the student needs to establish the relationship between angle of incidence and angle of refraction. This requires varying the independent variable (angle of incidence) while keeping all other factors constant (wavelength, glass type, surface quality). Glass thickness doesn't affect refraction at the air-glass interface. Choice B tests dispersion, not Snell's law. Choice C would test how refractive index varies with material. Choice D introduces unnecessary variables that could obscure the fundamental relationship.

Question 15

When designing an experiment to measure the Young's modulus of a wire using Hooke's law, a student must choose between two approaches: (I) applying increasing loads and measuring total extension, or (II) applying and removing loads cyclically while measuring extension. Which approach is preferable and why?

Approach I, because it provides more data points across a wider range of stresses for better statistical analysis
Approach II, because it allows detection of plastic deformation and ensures measurements stay within the elastic limit (correct answer)
Approach I, because cyclic loading introduces fatigue effects that would systematically alter the material properties being measured
Approach II, because averaging the loading and unloading data reduces random measurement errors in the extension readings

Explanation: Young's modulus (

E = \frac{\sigma}{\epsilon} = \frac{FL_0}{A\Delta L}

) is only valid in the elastic region where Hooke's law applies. Approach II (cyclic loading) reveals whether the material returns to its original length, indicating elastic behavior. If plastic deformation occurs, the unloading curve differs from loading, warning that the elastic limit was exceeded. Choice A overlooks the fundamental requirement of staying elastic. Choice C incorrectly assumes significant fatigue in a few cycles. Choice D mentions error reduction but misses the primary benefit of detecting plastic deformation.

Question 16

A student designs an experiment to measure the speed of sound in air by analyzing the resonance frequencies of a tube closed at one end. The tube length can be adjusted, and a speaker provides sound waves. What is the most significant experimental limitation that could affect the accuracy of the speed calculation?

Background noise in the laboratory interferes with the detection of resonance conditions at the various tube lengths
Room temperature fluctuations during the experiment will cause small variations in the actual sound speed being measured
The speaker produces harmonics in addition to the fundamental frequency, making it difficult to identify the resonance frequency
The finite diameter of the tube causes the effective length to differ from the measured length by an end correction factor (correct answer)

Explanation: When analyzing resonance in closed tubes, you're measuring standing wave patterns where the tube length relates to specific wavelengths. The fundamental resonance occurs when the tube length equals one-quarter wavelength, with subsequent resonances at odd multiples. Using the relationship

v = f\lambda

, you can calculate sound speed from the frequency and wavelength data. The most significant limitation is D - the finite diameter creates an end correction that makes the effective acoustic length longer than the physical tube length. At the open end, the sound wave extends slightly beyond the tube opening (typically about 0.6 times the radius), meaning your measured length systematically underestimates the true acoustic length. This creates a consistent error in all wavelength calculations, directly affecting your speed calculation. A is incorrect because background noise, while annoying, doesn't systematically bias your length measurements - you can still identify resonance peaks with careful observation. B represents a real but minor effect since temperature changes during a typical lab session cause only small speed variations (about 0.6 m/s per degree Celsius). C is wrong because harmonics actually help confirm resonance conditions rather than obscure them - multiple frequency components will all show enhanced amplitude at true resonance. Study tip: In IB Physics practicals involving wave measurements, always consider geometric factors that affect the relationship between measured and effective lengths. End corrections are a classic source of systematic error in acoustic experiments, so mention this limitation when discussing experimental uncertainties.

Question 17

An experiment investigates how the magnetic field strength at the center of a solenoid depends on the current. The student plans to use solenoids with different numbers of turns per unit length. Which approach would best isolate the current dependence?

Use multiple solenoids with different turn densities, measuring field versus current for each, then average all results together
Use a single solenoid with fixed turn density, vary only the current, and compare results to the theoretical prediction $B = \mu_0 nI$
Use multiple solenoids with different turn densities, plot $B/n$ versus current for each, and verify all data collapse to the same line (correct answer)
Use multiple solenoids with different turn densities, measure field versus current for each separately, and compare slopes to verify they scale with turn density

Explanation: The theoretical relationship

B = \mu_0 nI

predicts that

B/n

should be proportional to current with the same proportionality constant (

\mu_0

) for all solenoids. Plotting

B/n

I

for different turn densities tests whether all data collapse to a single line, providing strong evidence for the theoretical relationship. Choice A loses information by averaging. Choice B uses limited data from one solenoid. Choice D requires comparing slopes, which is less definitive than demonstrating data collapse and doesn't directly test the functional form.

Question 18

A student investigating the photoelectric effect plans to measure the maximum kinetic energy of photoelectrons using different wavelengths of incident light. Which experimental consideration is most critical for obtaining reliable results that can verify Einstein's photoelectric equation?

Ensuring the metal surface is clean and unoxidized, and using monochromatic light sources with precisely known wavelengths (correct answer)
Using high-intensity light sources to maximize the number of photoelectrons emitted for better statistical accuracy
Maintaining constant temperature of the metal surface throughout all measurements to prevent thermal effects
Using a variety of different metals with different work functions to test the universality of the photoelectric equation

Explanation: Einstein's equation

KE_{max} = hf - \phi

requires accurate measurement of photon energy (

hf = hc/\lambda

) and maximum kinetic energy. Surface contamination changes the effective work function, and non-monochromatic light makes photon energy uncertain. Choice B misunderstands that intensity affects the number of photoelectrons, not their maximum energy. Choice C is less critical since the work function temperature dependence is usually small over reasonable temperature ranges. Choice D tests a different aspect but isn't necessary for verifying the basic equation.

Question 19

When designing an experiment to measure the specific heat capacity of an unknown metal using the method of mixtures, which factor would most significantly compromise the validity of the results if not properly controlled?

Using distilled water instead of tap water as the calorimeter fluid for all trials in the experiment
Failing to account for the heat capacity of the calorimeter and stirrer in the energy balance calculations (correct answer)
Measuring the initial temperature of the metal to the nearest 0.5°C rather than 0.1°C consistently
Using metal samples with slightly different masses between trials while recording each mass accurately

Explanation: The calorimeter and stirrer absorb significant thermal energy during the mixing process. Ignoring their heat capacity introduces a systematic error that makes the calculated specific heat capacity consistently too low, as the energy balance equation

m_m c_m \Delta T_m = (m_w c_w + C_{cal}) \Delta T_w

requires the calorimeter heat capacity

C_{cal}

. Choice A is actually better practice (distilled water has known properties). Choice C affects precision but not validity if applied consistently. Choice D is acceptable experimental practice as long as masses are recorded.

Question 20

An investigation aims to determine the relationship between the power dissipated in a resistor and the applied voltage. A student measures current and voltage across various resistors while keeping each resistor at constant temperature. Which analysis approach would most effectively distinguish between $P \propto V$ and $P \propto V^2$ ?

Plot power versus voltage on linear scales and determine whether the relationship appears linear or quadratic based on visual inspection
Calculate the correlation coefficient between power and voltage, then between power and voltage squared, choosing the higher correlation
Plot $\log(P)$ versus $\log(V)$ and determine the slope; a slope of 1 indicates $P \propto V$ , while a slope of 2 indicates $P \propto V^2$ (correct answer)
Plot power versus voltage and fit both linear and quadratic functions, comparing the residuals to determine which model fits better

Explanation: For a power law relationship

P = kV^n

, taking logarithms gives

\log(P) = \log(k) + n\log(V)

. A log-log plot yields a straight line with slope

n

. This method directly determines the exponent and works well even with experimental scatter. Choice A relies on subjective visual assessment and may be ambiguous. Choice B measures correlation strength but both relationships could have high correlations. Choice D compares specific functional forms but doesn't directly determine the power law exponent, and the quadratic fit assumes

P \propto V^2

rather than testing it.