Topic 1: Measurements and uncertainties

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. 

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

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

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

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 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.

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 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.

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.

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 $y$?

Determine the fundamental SI unit for k.

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

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

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

Identify the fundamental units of $\gamma$.

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate 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.

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.

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 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.

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 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.

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

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.

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

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.

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

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Determine the fundamental SI unit for a.

Determine the fundamental SI unit for a.

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 $y$?

Determine the fundamental SI unit for k.

Determine the fundamental SI unit for k.

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

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

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

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

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

Identify the fundamental units of $\gamma$.

Identify the fundamental units of $\gamma$.

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

Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate 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.

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.

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 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.

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.

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 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.

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.

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 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 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 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.

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

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

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.

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.

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

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 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.

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

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

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Determine the fundamental SI unit for a.

Determine the fundamental SI unit for a.

Determine the fundamental SI unit for a.

Determine the fundamental SI unit for a.

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. 

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. 

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

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

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

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

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

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.

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 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 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.

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.

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 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.

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.

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.

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.

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

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

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

State the unit of K.

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

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

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

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

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

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

State the unit of c.

Suggest whether the data are consistent with the theoretical prediction.

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 %

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

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

Calculate the percentage error in the measured value of g.

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

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).

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 %

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

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

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.

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

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

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

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

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.  $\text{2.4} \text{cm}$

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 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

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 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 %

A rectangular sheet of paper has dimensions of (30.0 ± 0.5) cm and (20.0 ± 0.5) cm.

What is the percentage uncertainty of the perimeter of the paper?

A.  1 %

B.  2 %

C.  2.5 %

D.  4 %

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

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 %

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

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

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

Calculate the percentage error in the measured value of g.

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

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).

Calculate the percentage error in the measured value of g.

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

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).

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 %

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

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

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

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

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.

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

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

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.

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

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

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

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

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

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

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.  $\text{2.4} \text{cm}$

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 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

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 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 %

A rectangular sheet of paper has dimensions of (30.0 ± 0.5) cm and (20.0 ± 0.5) cm.

What is the percentage uncertainty of the perimeter of the paper?

A.  1 %

B.  2 %

C.  2.5 %

D.  4 %

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

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

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

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

State the unit of K.

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

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

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

State the unit of K.

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

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

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

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

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

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

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

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

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

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

This relationship can also be written as follows.

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

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

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

State the unit of c.

Suggest whether the data are consistent with the theoretical prediction.

State the unit of c.

Suggest whether the data are consistent with the theoretical prediction.

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

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

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

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

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?

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.

Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.

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

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

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

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?

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.

Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.

The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.

Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.

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

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

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

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