There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

Draw on the graph the line of best fit for the data.

State how the value of K can be obtained from the graph.

Two different experiments, P and Q, generate two sets of data to confirm the proportionality of variables $x$ and $y$. The graphs for the data from P and Q are shown. The maximum and minimum gradient lines are shown for both sets of data.

What is true about the systematic error and the uncertainty of the gradient when P is compared to Q?

The equation in (b) may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$. Suggest why this will be an unreliable estimate of the pressure.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

A student is verifying the equation

$$x=\frac{2\lambda Y}{z}$$

The percentage uncertainties are:

What is the percentage uncertainty in x?

A. 5 %

B. 15 %

C. 25 %

D. 30 %

Estimate the power input to the heating element. State an appropriate unit for your answer.

State the fundamental SI unit for your answer to (a)(i).

In a different experiment a student investigates the dependence of the period T of a simple pendulum on the amplitude of oscillations θ. The graph shows the variation of $\frac{T}{T_0}$ with θ, where T₀ is the period for small amplitude oscillations.

The period may be considered to be independent of the amplitude θ as long as . Determine the maximum value of θ for which the period is independent of the amplitude.

The uncertainty in reading a laboratory thermometer is 0.5 °C. The temperature of a liquid falls from 20 °C to 10 °C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A.  2.5 %

B.  5 %

C.  7.5 %

D.  10 %

The intensity of a wave can be defined as the energy per unit area per unit time. What is the unit of intensity expressed in fundamental SI units?

A.  kg m⁻²s⁻¹

B.  kg m²s⁻³

C.  kg s⁻²

D.  kg s⁻³

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

The magnitude of the resultant of two forces acting on a body is 12 N. Which pair of forces acting on the body can combine to produce this resultant?

A.  1 N and 2 N

B.  1 N and 14 N

C.  5 N and 6 N

D.  6 N and 7 N

The graphs show the variation of the displacement y of a medium with distance $x$ and with time t for a travelling wave.

What is the speed of the wave?

A.   0.6 m s^–1

B.   0.8 m s^–1

C.   600 m s^–1

D.   800 m s^–1

A student forms a hypothesis that the period of one oscillation P is given by:

$$P=\frac{K}{\sqrt{B}}$$

where K is a constant.

Determine the value of K using the point for which B = 0.005 T.

State the uncertainty in K to an appropriate number of significant figures. 

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

At a particular instant in the flight the glider is losing 1.00 m of vertical height for every 6.00 m that it goes forward horizontally. At this instant, the horizontal speed of the glider is 12.5 m s^–1. Calculate the velocity of the glider. Give your answer to an appropriate number of significant figures.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

State the unit of K.

Explain the disadvantage that a graph of I versus $\frac{1}{x^2}$ has for the analysis in (b)(i) and (b)(ii).

Calculate the percentage error in the measured value of g.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

A student models the relationship between the pressure p of a gas and its temperature T as p = $x$ + $y$T.

The units of p are pascal and the units of T are kelvin. What are the fundamental SI units of $x$ and $y$?

Suggest whether the data are consistent with the theoretical prediction.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Deduce the value of g and its absolute uncertainty for this experiment.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

Suggest why it is unlikely that the relation between d and $\lambda$ is linear.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

Determine P, to the correct number of significant figures including its unit.

A student suggests that to get a more accurate value of L_v the experiment should be performed twice using different heating rates. With voltage and current V₁, I₁ the mass of water that vaporized in time t is m₁. With voltage and current V₂, I₂ the mass of water that vaporized in time t is m₂. The student now uses the expression

$$L_v=\frac{\left(V_1{I}_1-V_2{I}_2\right)t}{m_1-m_2}$$

to calculate L_v. Suggest, by reference to heat losses, why this is an improvement.

The experiment is repeated using a different gas in the glass jar. The pressure for both experiments is low and both gases can be considered to be ideal.

(i) Using the axes provided in (a), draw the expected graph for this second experiment.

(ii) Explain the shape and intercept of the graph you drew in (b)(i).

percentage uncertainty in d ².

Determine the fundamental SI unit for k.

Calculate the component of weight for the bicycle and girl acting down the slope.

A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 2.0 ±0.2 s. The depth of the well is calculated to be 20 m using d = $\frac{1}{2}$at ². The uncertainty in a is negligible.

What is the absolute uncertainty in d?

A.  ± 0.2 m

B.  ± 1 m

C.  ± 2 m

D.  ± 4 m

After taking measurements the student observes that the ammeter has a positive zero error. Explain what effect, if any, this zero error will have on the calculated value of the internal resistance in (b).

State what is meant by a zero error.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

State the fundamental SI unit of the constant a and of the constant b.

The following graph of p versus $\frac{1}{H}$ was obtained. Error bars were negligibly small.

The equation of the line of best fit is $p=a+\frac{b}{H}$.

Determine the value of b including an appropriate unit.

Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

Estimate C.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

(i) Outline why OY has a greater percentage uncertainty than OX for each pair of data points.

(ii) The refractive index of the water is given by $\frac{\mathrm{O}\mathrm{X}}{\mathrm{O}\mathrm{Y}}$when OX is small.

Calculate the fractional uncertainty in the value of the refractive index of water for OX = 1.8 cm.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

Identify the fundamental units of $\gamma$.

In order to find the uncertainty for $\gamma$, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

A. $\frac{2\mathrm{\Delta }R}{R}$

B. ${\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

C. $\frac{2\pi \mathrm{\Delta }R}{R}$

D. $\pi {\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

The expected value of $\gamma$ is $0.027$. Comment on your result.

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$$\omega =\frac{2\pi }{T}$$ 

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %

The percentage uncertainty for $\gamma$ is $15\%$. State $\gamma$, with its absolute uncertainty.

A graph of the variation of OY with OX is plotted.

(i) Draw, on the graph, the error bars for OY when OX = 1.8 cm and when OY = 5.8 cm.

(ii) Determine, using the graph, the refractive index of the water in the container for values of OX less than 6.0 cm.

(iii) The refractive index for a material is also given by $\frac{\sin i}{\sin r}$ where i is the angle of incidence and r is the angle of refraction.

Outline why the graph deviates from a straight line for large values of OX.

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.

State the unit of c.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

The charge per unit area on the surface of the wall is σ. It can be shown that the electric field strength E due to the charge on the wall is given by the equation

$E=\frac{\sigma }{2{\epsilon }_0}$.

Demonstrate that the units of the quantities in this equation are consistent.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Using the following equation

$$\text{acceleration due to gravity}=\frac{2\times \text{distance fallen by centre of mass of sphere}}{{\text{(measured time to fall)}}^{\text{2}}}$$

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.

Suggest why the student’s data supports the theoretical prediction.

A student measures the length l and width w of a rectangular table top.

What is the absolute uncertainty of the perimeter of the table top?

A.  $0.3 \text{cm}$

B.  $0.6 \text{cm}$

C.  $\text{1.2} \text{cm}$

D.  $\text{2.4} \text{cm}$

What is the unit of power expressed in fundamental SI units?

A.  ${\text{kg\hspace{0.05em}m\hspace{0.05em}s}}^{-3}$

B.  ${\text{kg\hspace{0.05em}m\hspace{0.05em}s}}^{-1}$

C.  ${\text{kg\hspace{0.05em}m}}^2{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{kg\hspace{0.05em}m}}^2{\text{\hspace{0.05em}s}}^{-3}$

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The measurements of $T$ were collected five times. Explain how repeated measurements of $T$ reduced the random error in the final experimental value of $mr$.

Estimate the resistivity of the material of the wire. Give your answer to an appropriate number of significant figures.

State why the experiment is repeated with different values of $W$.

The charge per unit area on the surface of the wall is σ. It can be shown that the electric field strength E due to the charge on the wall is given by the equation

$E=\frac{\sigma }{2{\epsilon }_0}$.

Demonstrate that the units of the quantities in this equation are consistent.

The player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of $1.40 {\text{m\hspace{0.05em}s}}^{-1}$. The radius of the ball is $0.11 \text{m}$. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.

Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.

Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.

An object has a weight of 6.10 × 10² N. What is the change in gravitational potential energy of the object when it moves through 8.0 m vertically?

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

In a simple pendulum experiment, a student measures the period T of the pendulum many times and obtains an average value T = (2.540 ± 0.005) s. The length L of the pendulum is measured to be L = (1.60 ± 0.01) m.

Calculate, using $g=\frac{4{\pi }^{2}L}{T^2}$, the value of the acceleration of free fall, including its uncertainty. State the value of the uncertainty to one significant figure.

fractional uncertainty in d.

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A.     ${\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

B.     $3\frac{\mathrm{\Delta }r}{r}$

C.     $4\pi \frac{\mathrm{\Delta }r}{r}$

D.     $4\pi {\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

When d = 0.200 mm, s = 0.9 mm and D = 280 mm, determine the percentage uncertainty in the wavelength.

A ball of mass (50 ± 1) g is moving with a speed of (25 ± 1) m s⁻¹. What is the fractional uncertainty in the momentum of the ball?

A.  0.02

B.  0.04

C.  0.06

D.  0.08

The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.

The radius of a circle is measured to be (10.0 ± 0.5) cm. What is the area of the circle?

A.  (314.2 ± 0.3) cm²

B.  (314 ± 1) cm²

C.  (314 ± 15) cm²

D.  (314 ± 31) cm²