Tools

Calculate the percentage uncertainty in the value of A.

Suggest an appropriate measuring instrument for determining b.

To determine T more precisely, the student measures the total time for 20 oscillations and divides by 20.

Explain why this is preferable to measuring the time for just one oscillation.

To determine T more precisely, the student measures the total time for 20 oscillations and divides by 20.

Explain why this is preferable to measuring the time for just one oscillation.

Calculate the percentage uncertainty in the value of A.

Suggest an appropriate measuring instrument for determining b.

Suggest an appropriate measuring instrument for determining b.

Calculate the percentage uncertainty in the value of A.

Calculate the percentage uncertainty in the value of A.

Suggest an appropriate measuring instrument for determining b.

Suggest an appropriate measuring instrument for determining b.

To determine T more precisely, the student measures the total time for 20 oscillations and divides by 20.

Explain why this is preferable to measuring the time for just one oscillation.

To determine T more precisely, the student measures the total time for 20 oscillations and divides by 20.

Explain why this is preferable to measuring the time for just one oscillation.

Calculate the percentage uncertainty in the value of A.

Suggest an appropriate measuring instrument for determining b.

Suggest an appropriate measuring instrument for determining b.

Calculate the percentage error in the measured value of g.

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

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 %

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

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

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.

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 $y$?

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters.

Which quantities should the student plot on the $x$-axis and the $y$-axis of a graph to obtain a straight line?

Suggest whether the data are consistent with the theoretical prediction.

Show that the value of $\gamma$  is about 0.03.

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.

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.

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

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

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

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 %

Determine the fundamental SI unit for a.

Determine the fundamental SI unit for a.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of $E$ are kg m⁻¹s⁻².

Calculate $x$ and $y$.

Suggest an appropriate measuring instrument for determining b.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in nm, $\lambda$.

The student moves the screen closer to the double slit and repeats the measurements. The instruments used to make the measurements are unchanged.

Discuss the effect this movement has on the fractional uncertainty in the value of $\lambda$.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Determine, using the graph, whether the gas acts as an ideal gas.

Masses P and Q, are measured to be (30 ± 1) g and (20 ± 1) g respectively. Which of the following expressions gives the least percentage uncertainty?

A.  P + Q

B.  P − Q

C.  P × Q

D.  $\frac{P}{Q}$

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

Deduce the unit of μ in terms of fundamental SI units.

The percentage uncertainty of the gradient is 6.0 %. The frequency $f$ of the wave is (60.0 ± 2.0 %) Hz.

Estimate, using the answer to (b)(iv), μ for the string. Include the percentage uncertainty of μ in your answer.

Draw and label on diagram B the forces acting on the sphere just after it has been released.

Deduce the unit of μ in terms of fundamental SI units.

The percentage uncertainty of the gradient is 6.0 %. The frequency $f$ of the wave is (60.0 ± 2.0 %) Hz.

Estimate, using the answer to (b)(iv), μ for the string. Include the percentage uncertainty of μ in your answer.

Show, using two suitable data points from the table, that the student’s initial hypothesis is not supported.

State the unit for k.

Draw on the graph the position of the missing point for the Δp value of 40 kPa.

Calculate the absolute uncertainty in $F_{\max }^3$ for Δp = 30 kPa. State an appropriate number of significant figures for your answer.

Draw the absolute uncertainty determined in part (d)(i) as an error bar on the graph.

Show, using two suitable data points from the table, that the student’s initial hypothesis is not supported.

State the unit for k.

Draw on the graph the position of the missing point for the Δp value of 40 kPa.

Calculate the absolute uncertainty in $F_{\max }^3$ for Δp = 30 kPa. State an appropriate number of significant figures for your answer.

Draw the absolute uncertainty determined in part (d)(i) as an error bar on the graph.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of $E$ are kg m⁻¹s⁻².

Calculate $x$ and $y$.

Suggest an appropriate measuring instrument for determining b.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Calculate the percentage error in the measured value of g.

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

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 %

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

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

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.

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 $y$?

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters.

Which quantities should the student plot on the $x$-axis and the $y$-axis of a graph to obtain a straight line?

Suggest whether the data are consistent with the theoretical prediction.

Show that the value of $\gamma$  is about 0.03.

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.

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.

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

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

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

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 %

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.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of $E$ are kg m⁻¹s⁻².

Calculate $x$ and $y$.

Suggest an appropriate measuring instrument for determining b.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of $E$ are kg m⁻¹s⁻².

Calculate $x$ and $y$.

Suggest an appropriate measuring instrument for determining b.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Determine, using the graph, whether the gas acts as an ideal gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Calculate, in nm, $\lambda$.

The student moves the screen closer to the double slit and repeats the measurements. The instruments used to make the measurements are unchanged.

Discuss the effect this movement has on the fractional uncertainty in the value of $\lambda$.

Calculate, in nm, $\lambda$.

The student moves the screen closer to the double slit and repeats the measurements. The instruments used to make the measurements are unchanged.

Discuss the effect this movement has on the fractional uncertainty in the value of $\lambda$.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Determine, using the graph, whether the gas acts as an ideal gas.

Determine, using the graph, whether the gas acts as an ideal gas.

Masses P and Q, are measured to be (30 ± 1) g and (20 ± 1) g respectively. Which of the following expressions gives the least percentage uncertainty?

A.  P + Q

B.  P − Q

C.  P × Q

D.  $\frac{P}{Q}$

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

Deduce the unit of μ in terms of fundamental SI units.

The percentage uncertainty of the gradient is 6.0 %. The frequency $f$ of the wave is (60.0 ± 2.0 %) Hz.

Estimate, using the answer to (b)(iv), μ for the string. Include the percentage uncertainty of μ in your answer.

Draw and label on diagram B the forces acting on the sphere just after it has been released.

Deduce the unit of μ in terms of fundamental SI units.

The percentage uncertainty of the gradient is 6.0 %. The frequency $f$ of the wave is (60.0 ± 2.0 %) Hz.

Estimate, using the answer to (b)(iv), μ for the string. Include the percentage uncertainty of μ in your answer.

Show, using two suitable data points from the table, that the student’s initial hypothesis is not supported.

State the unit for k.

Draw on the graph the position of the missing point for the Δp value of 40 kPa.

Calculate the absolute uncertainty in $F_{\max }^3$ for Δp = 30 kPa. State an appropriate number of significant figures for your answer.

Draw the absolute uncertainty determined in part (d)(i) as an error bar on the graph.

Show, using two suitable data points from the table, that the student’s initial hypothesis is not supported.

State the unit for k.

Draw on the graph the position of the missing point for the Δp value of 40 kPa.

Calculate the absolute uncertainty in $F_{\max }^3$ for Δp = 30 kPa. State an appropriate number of significant figures for your answer.

Draw the absolute uncertainty determined in part (d)(i) as an error bar on the graph.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of $E$ are kg m⁻¹s⁻².

Calculate $x$ and $y$.

Suggest an appropriate measuring instrument for determining b.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.

Calculate the largest fractional uncertainty in T for these data.

Determine A by drawing the line of best fit.

Theory predicts that

$d\propto \frac{W^x{L}^y}{EI}$

where $E$ and $I$ are constants. The fundamental units of $I$ are m⁴ and those of E are kg m⁻¹ s⁻².

Calculate $x$ and $y$.

Calculate the percentage uncertainty in the value of A.