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?

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

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 %

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.

State the unit of K.

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.

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 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.

percentage uncertainty in d ².

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.

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.

(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.

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.

State the unit of c.

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.

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.  $\text{2.4} \text{cm}$

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 $W$.

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 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