A1. Data analysis question.
The photograph below shows a magnified image of a dark central disc surrounded by concentric dark rings. These rings were produced as a result of interference of monochromatic light.
The graph below shows how the ring diameter D varies with the ring number n.The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the photograph. Error bars for the diameter D are shown.
(a) State one piece of evidence that shows that D is not proportional to n.
(b) On the graph opposite, draw the line of best-fit for the data points.
(c) Theory suggests that D2 = kn. A graph of D2 against n is shown below. Error bars are shown for the first and last data points only.
(i) Using the graph on page 2, calculate the percentage uncertainty in D2, of the ring n = 7.
(ii) Based on the graph opposite, state one piece of evidence that supports the relationship D2 = kn.
(iii) Use the graph opposite to determine the value of the constant k, as well as its uncertainty.
(iv) State the unit for the constant k.
A2. This question is about motion in a magnetic field.
An electron, that has been accelerated from rest by a potential difference of 250 V, enters a region of magnetic field of strength 0.12 T that is directed into the plane of the page.
(a) The electron’s path while in the region of magnetic field is a quarter circle. Show that the
(i) speed of the electron after acceleration is 9.4×106ms−1.
(ii) radius of the path is 4.5×10-4 m.
(b) The diagram below shows the momentum of the electron as it enters and leaves the region of magnetic field. The magnitude of the initial momentum and of the final momentum is 8.6×10−24Ns.
(i) On the diagram above, draw an arrow to indicate the vector representing the change in the momentum of the electron.
(ii) Show that the magnitude of the change in the momentum of the electron is 1.2×10−23Ns.
(iii) The time the electron spends in the region of magnetic field is 7.5 ×10−11s. Estimate the magnitude of the average force on the electron.
A3. This question is about circular motion.
A ball of mass 0.25 kg is attached to a string and is made to rotate with constant speed v along a horizontal circle of radius r = 0.33m. The string is attached to the ceiling and makes an angle of 30° with the vertical.
(a) (i) On the diagram above, draw and label arrows to represent the forces on the ball in the position shown.
(ii) State and explain whether the ball is in equilibrium.
(b) Determine the speed of rotation of the ball.