Total marks: 100 · Duration: 2 hours 30 minutes
Instructions to candidates
- This paper consists of SIX compulsory questions in two sections. Answer ALL questions.
- Section A has THREE structured questions worth 55 marks. Question 1 is a data analysis question worth 25 marks; do NOT spend more than 30 minutes on it.
- Section B has THREE extended response questions worth 15 marks each (45 marks).
- In the January 2027 sitting this paper is "hybrid": you read the questions on screen and write your answers in the answer booklet. Graph paper is provided in the booklet.
- A silent, non-programmable calculator may be used. Show all working and give units with your answers.
- Where needed, use: speed of light in air c = 3.00 × 10⁸ m s⁻¹; specific heat capacity of water = 4200 J kg⁻¹ °C⁻¹; specific latent heat of fusion of ice = 3.34 × 10⁵ J kg⁻¹.
Paper
Section A — Structured Questions (55 marks)
Question 1 (data analysis)
Andre investigated how the period T of a simple pendulum depends on its length l. For each length he timed 20 complete oscillations with a stopwatch. His results are shown in the table; some values have been left blank.
| Length l / m | Time for 20 oscillations / s | Period T / s | T² / s² |
|---|---|---|---|
| 0.20 | 18.0 | 0.900 | 0.810 |
| 0.40 | 25.4 | 1.270 | 1.613 |
| 0.60 | 31.1 | ||
| 0.80 | 35.9 | ||
| 1.00 | 40.1 | 2.005 | 4.020 |
(a) Explain why Andre timed 20 oscillations instead of a single oscillation. (1 mark)
(b) Copy and complete the table by calculating T and T² for the lengths 0.60 m and 0.80 m. (3 marks)
(c) On graph paper in your answer booklet, plot a graph of T² (vertical axis) against l (horizontal axis) and draw the line of best fit. (4 marks)
(d) Determine the gradient of your line, showing clearly the values you used. (2 marks)
(e) The period of a simple pendulum is related to its length by T² = (4π² ÷ g) × l. Use your gradient to calculate a value for g, the acceleration due to gravity. (2 marks)
(f) Use your graph to find the length of a pendulum with a period of 1.50 s. (2 marks)
(g) State TWO precautions Andre should take to obtain accurate results. (2 marks)
(h) Plan and design an experiment to test whether the mass of the pendulum bob affects the period. Your answer should include:
(i) a hypothesis (1 mark)
(ii) the method, including the apparatus you would use (3 marks)
(iii) the variable you would keep constant (1 mark)
(iv) a results table with suitable headings (1 mark)
(v) the results you would expect if your hypothesis is correct (1 mark)
(i) A classmate claims that doubling the length of a pendulum doubles its period. Use Andre's results to show whether this claim is correct. (2 marks)
Total 25 marks
Question 2
A route taxi of total mass 2400 kg, including its passengers, starts from rest at a bus stop. It accelerates uniformly to 15 m s⁻¹ in 6.0 s, travels at this constant speed for 20 s, then decelerates uniformly to rest in 5.0 s.
(a) Calculate the acceleration of the taxi during the first 6.0 s. (2 marks)
(b) Calculate the total distance travelled by the taxi. (3 marks)
(c) Calculate the resultant force on the taxi while it is accelerating. (2 marks)
(d) Calculate the braking force needed to bring the taxi to rest in 5.0 s. (2 marks)
(e) Use Newton's first law of motion to explain why a standing passenger lurches forward when the taxi brakes. (2 marks)
(f) Calculate the momentum of the taxi while it travels at constant speed. (2 marks)
(g) Explain, in terms of force and time, how a seat belt reduces injury in a sudden stop. (2 marks)
Total 15 marks
Question 3
Many Caribbean homes use rooftop solar water heaters.
(a) Define specific heat capacity. (1 mark)
(b) The storage tank of a solar water heater holds 150 kg of water. On a sunny day the water temperature rises from 27 °C to 57 °C. Calculate the energy absorbed by the water. (2 marks)
(c) The collector panels receive solar energy at an average rate of 2.5 kW for 6.0 hours. Calculate the total solar energy received. (2 marks)
(d) Calculate the efficiency of the solar water heater. (2 marks)
(e) An ice cooler contains 2.0 kg of ice at 0 °C. Calculate the energy needed to melt all of the ice. (2 marks)
(f) Use the kinetic theory to explain why the temperature of the ice stays at 0 °C while it is melting, even though energy is being absorbed. (2 marks)
(g) Explain why the collector panels of the solar water heater are painted matt black. (2 marks)
(h) Explain why the storage tank is surrounded by a layer of foam insulation. (2 marks)
Total 15 marks
Section B — Extended Response (45 marks)
Question 4
(a) Distinguish between transverse and longitudinal waves, and give ONE example of each. (3 marks)
(b) A radio station broadcasts at a frequency of 90.0 MHz. Calculate the wavelength of its radio waves. (2 marks)
(c) A ray of light passes from air into a glass block of refractive index 1.50 at an angle of incidence of 40°. Calculate the angle of refraction. (3 marks)
(d) (i) Calculate the critical angle for this glass. (2 marks)
(ii) State the TWO conditions needed for total internal reflection to occur. (2 marks)
(iii) State ONE practical use of total internal reflection. (1 mark)
(e) A fishing boat's echo sounder sends a pulse of ultrasound straight down. The echo from the sea bed returns 0.040 s later. The speed of sound in sea water is 1500 m s⁻¹. Calculate the depth of the water. (2 marks)
Total 15 marks
Question 5
(a) State Ohm's law. (1 mark)
(b) A 12 V battery of negligible internal resistance is connected in series with a 4.0 Ω resistor and a parallel pair of resistors, one of 6.0 Ω and one of 3.0 Ω.
(i) Calculate the total resistance of the circuit and the current drawn from the battery. (3 marks)
(ii) Calculate the potential difference across the parallel pair and the current in EACH of the 6.0 Ω and 3.0 Ω resistors. (3 marks)
(iii) Calculate the power dissipated in the 4.0 Ω resistor. (2 marks)
(c) A 1.5 kW air conditioner runs for 8 hours a day. Calculate the cost of running it for 30 days if electricity costs $0.90 per kilowatt-hour. (3 marks)
(d) Explain why the lamps in a house are connected in parallel rather than in series. (3 marks)
Total 15 marks
Question 6
(a) Compare alpha, beta and gamma radiation in terms of their nature, their charge and their penetrating ability. (3 marks)
(b) The activity of a radioactive sample falls from 800 Bq to 100 Bq in 24 days. Calculate its half-life. (2 marks)
(c) Iodine-131 (atomic number 53) decays by beta emission to an isotope of xenon (atomic number 54). Write the nuclear equation for this decay. (2 marks)
(d) Radioactive tracers are used in medicine to examine organs inside the body. Explain why a tracer should be a gamma emitter with a short half-life. (3 marks)
(e) State TWO precautions taken by hospital staff who handle radioactive sources. (2 marks)
(f) A transformer steps down 240 V a.c. to 12 V. Its primary coil has 2000 turns.
(i) Calculate the number of turns on the secondary coil. (2 marks)
(ii) Explain why a transformer does not work with a steady direct current. (1 mark)
Total 15 marks