Paper 4 style practice paper: Theory (Extended) — question paper

Section A: Structured questions[40 marks]

Answer all questions in the spaces provided. The marks in Section A total 40.

1. 1

   A stone falls freely from rest near the Earth’s surface, where the acceleration of free fall is 9.8 m/s². Air resistance is negligible until stated otherwise.

   1. (a)

      Calculate the speed of the stone 3.0 s after it is released.

      [2]
   2. (b)

      Calculate the distance fallen during these first 3.0 s.

      [3]
   3. (c)

      In practice air resistance acts on the stone. State and explain how the stone’s acceleration changes as it falls faster.

      [1]
2. 2

   A delivery drone of mass 2.5 kg rises vertically, accelerating from rest to a speed of 8.0 m/s after climbing 4.0 m. Take g = 9.8 N/kg.

   1. (a)

      Calculate the gain in kinetic energy of the drone.

      [2]
   2. (b)

      The gain in kinetic energy equals the work done by the resultant force over the 4.0 m climb. Calculate the resultant force.

      [2]
   3. (c)

      Explain why the upward thrust of the drone’s rotors must be greater than its weight during the climb, and calculate the thrust.

      [4]
3. 3

   A hand pump traps air at a pressure of 100 kPa in a volume of 120 cm³. The pump’s outlet is blocked and the handle is pushed in slowly, at constant temperature, until the volume is 40 cm³.

   1. (a)

      Calculate the new pressure of the trapped air.

      [3]
   2. (b)

      Explain the pressure rise using the kinetic particle model.

      [3]
   3. (c)

      The trapped air is now heated while the volume stays at 40 cm³. State and explain what happens to the pressure.

      [2]
4. 4

   A 12 V, 36 W immersion heater warms 0.60 kg of oil in a lagged container. The oil’s specific heat capacity is 2000 J/(kg °C) and it starts at 15 °C.

   1. (a)

      Calculate the current through the heater.

      [2]
   2. (b)

      The heater runs for 5.0 minutes. Calculate the energy delivered to the oil.

      [2]
   3. (c)

      Calculate the temperature rise of the oil, assuming all the energy enters it.

      [2]
   4. (d)

      The measured rise is only 8.0 °C. Suggest one reason for the difference.

      [2]
5. 5

   A ray of light in air strikes a rectangular glass block (refractive index 1.5) at an angle of incidence of 40°.

   1. (a)

      Calculate the angle of refraction inside the glass.

      [3]
   2. (b)

      Calculate the critical angle for the glass–air boundary.

      [2]
   3. (c)

      The ray reaches the far, vertical face of the block at an angle of incidence of 65°. State and explain what happens to the ray there.

      [3]
   4. (d)

      State one practical application of total internal reflection.

      [2]

Section B: Structured questions[40 marks]

Answer all questions in the spaces provided. The marks in Section B total 40.

1. 6

   A student builds a circuit from a 12 V battery, an ammeter, a lamp marked 12 V, 24 W, and a fixed resistor R, all in series. The ammeter reads 1.5 A.

   1. (a)

      Calculate the resistance of the lamp when it is working normally.

      [2]
   2. (b)

      Explain why the lamp is dim in this circuit.

      [3]
   3. (c)

      Calculate the total resistance of the circuit.

      [2]
   4. (d)

      Calculate the resistance of R and the p.d. across it.

      [3]
2. 7

   A power station produces 800 MW and feeds a step-up transformer that raises the voltage from 25 kV to 400 kV for transmission through cables of total resistance 3.0 Ω. Assume 100% efficiency in the transformer.

   1. (a)

      Calculate the current in the transmission cables.

      [2]
   2. (b)

      Calculate the power lost as heat in the cables.

      [2]
   3. (c)

      Calculate the current that would flow in the same cables if the power were transmitted at 25 kV instead, and the corresponding cable loss.

      [4]
   4. (d)

      Explain why the transformer only works with an alternating input.

      [2]
3. 8

   A radioactive isotope X of sodium has a half-life of 15 hours and emits beta radiation. Its nuclide notation is ²⁴₁₁X. A detector near a fresh sample reads 6400 counts/min, and the background count rate is 100 counts/min.

   1. (a)

      Calculate the number of neutrons in one nucleus of X.

      [1]
   2. (b)

      Calculate the corrected count rate after 60 hours.

      [3]
   3. (c)

      Write the decay equation for the beta decay of X, given that the daughter nucleus is magnesium (Mg, Z = 12).

      [3]
   4. (d)

      Beta radiation is deflected in a magnetic field but gamma radiation is not. Explain why.

      [3]
4. 9

   A satellite orbits a planet of uniform surface gravitational field strength 4.0 N/kg in a circular orbit of radius 8.0 × 10⁶ m with a period of 2.0 × 10⁴ s. The planet’s largest moon orbits at radius 4.0 × 10⁸ m.

   1. (a)

      Calculate the orbital speed of the satellite.

      [3]
   2. (b)

      The moon’s orbital radius is 50 times the satellite’s. State and explain what you can conclude about the moon’s orbital speed compared with the satellite’s, assuming both orbits are circular.

      [3]
   3. (c)

      Light from the planet’s own star takes 6.0 × 10³ s to reach the planet. Calculate the star–planet distance.

      [2]
   4. (d)

      The planet’s star is observed to have redshifted light. State what this tells us about the star, and about the Universe as a whole.

      [2]