Paper 1: Fundamentals of physics

A converging lens has focal length 0.25 m. What is its power?

An object is 0.30 m from a lens of focal length 0.10 m. Using 1/v = 1/u + 1/f (u = −0.30 m), the image distance is:

How many bits are needed to code 256 different levels?

An image has 1000 × 800 pixels, each coded with 8 bits. How many bits are needed?

A signal contains frequencies up to 20 kHz. What is the minimum sampling rate?

What is the conductance of a 50 Ω resistor?

Conductances of 0.010 S and 0.040 S are connected in parallel. The total conductance is:

A sensor's output changes by 0.50 V when the temperature changes by 10 K. Its sensitivity is:

The SI unit of the Young modulus is:

A force of 2000 N acts on a cross-section of 4.0 × 10⁻⁶ m². The stress is:

Which material is brittle?

Metals are ductile because:

A path difference of λ/2 gives a phase difference of:

What is the energy of a photon of frequency 5.0 × 10¹⁴ Hz?

An electron is accelerated through 100 V. Its kinetic energy gain is:

Light of 650 nm passes through slits 0.50 mm apart onto a screen 2.0 m away. The fringe spacing is:

The area under a velocity–time graph gives:

A car goes from rest to 20 m s⁻¹ in 8.0 s. Its mean acceleration is:

A ball is thrown up at 15 m s⁻¹. Its maximum height is about:

Forces of 3.0 N and 4.0 N act at right angles. The resultant is:

In a model ΔN = −λNΔt with N = 1000, λ = 0.10 s⁻¹ and Δt = 1.0 s, N after one step is:

A capacitor discharges with time constant 2.0 s. After 4.0 s the fraction of charge left is:

A 0.50 kg mass on a spring of stiffness 20 N m⁻¹ oscillates. The period is about:

A force of 4.0 N acts for 0.50 s. The change in momentum is:

At a distance 2R from the centre of a planet of radius R, g is:

The volume of a gas is halved at constant temperature. The pressure:

kT at 300 K is 0.026 eV. What is the Boltzmann factor for an energy of 0.10 eV?

The mean kinetic energy of a monatomic ideal gas particle is:

The flux linkage through a coil changes by 0.60 Wb turns in 0.20 s. The average emf is:

The unit of absorbed dose is the:

A camera image has 2048 × 1536 pixels, each coded with 24 bits. Calculate the number of bytes needed to store the image.

Explain how replacing each pixel's value by the median of its neighbours removes 'salt-and-pepper' noise, and one disadvantage.

A camera lens of focal length 50 mm focuses on a person 1.8 m tall standing 2.0 m away. Calculate the image distance and the height of the image.

Music is sampled at 44.1 kHz with 16 bits per sample in two channels. Calculate the bit rate and the storage for a 3.0-minute track in megabytes, and explain the choice of 44.1 kHz.

A signal varies over 2.0 V and the noise is 0.010 V. Calculate the number of distinguishable levels and the number of bits worth recording.

A temperature sensor is a thermistor in series with a fixed 2.2 kΩ resistor across 5.0 V. The output is across the fixed resistor. The thermistor's resistance is 4.7 kΩ at 20 °C and 2.2 kΩ at 40 °C. Calculate the output at each temperature and the mean sensitivity.

Sketch and describe the stress–strain graph for a ductile metal, identifying the Young modulus, yield point and ultimate tensile stress, and explain what toughness means.

A nylon line of diameter 0.30 mm and length 2.0 m extends by 40 mm under a load of 3.0 N. Calculate the Young modulus.

Explain, in terms of microstructure, why metals are tough but ceramics such as glass are brittle, and how glass can be made safer.

In a two-slit experiment, slits 0.40 mm apart give fringes 2.4 mm apart on a screen 1.5 m away. Calculate the wavelength and use phasors to explain why there is a bright fringe where the path difference is a whole number of wavelengths.

Electrons accelerated through 5.0 kV pass through a graphite film. Calculate their de Broglie wavelength and explain the pattern using the idea that quanta 'explore all paths'.

A red LED (650 nm) just starts to emit light at 1.9 V. Use this to estimate the Planck constant.

An 80 kg skydiver has drag D = 0.25v². Use a step-by-step model with Δt = 0.50 s, starting from rest, to find the velocity after 1.0 s, and calculate the terminal velocity.

A boat heads straight across a 60 m wide river at 3.0 m s⁻¹ relative to the water. The current is 1.5 m s⁻¹. Calculate the resultant velocity, the crossing time and how far downstream it lands.

A 1000 μF capacitor charged to 6.0 V discharges through 4.7 kΩ. Use one step of ΔQ = −(Q/RC)Δt with Δt = 1.0 s to estimate V after 1.0 s, compare with the exact value, and explain the difference.

Carbon-14 has a half-life of 5730 years. Living material has an activity of 0.25 Bq per gram of carbon. Calculate the age of a sample with activity 0.0625 Bq g⁻¹, and the activity of a sample 8000 years old.

Explain why capacitor discharge and radioactive decay are described by the same type of equation.

The Moon orbits at 3.84 × 10⁸ m from the Earth's centre with period 27.3 days. Calculate its centripetal acceleration and show it agrees with g/60² (the Moon is about 60 Earth radii away).

A rocket ejects 50 kg of exhaust gas per second at 2500 m s⁻¹. Calculate the thrust and explain it using conservation of momentum.

A reaction has activation energy 0.60 eV per particle. Calculate the ratio of the Boltzmann factors at 310 K and 300 K, and explain why this suggests the rate roughly doubles.

A balloon holds 0.012 m³ of helium at 100 kPa and 290 K. Calculate the number of atoms and their rms speed (mass of He atom 6.64 × 10⁻²⁷ kg).

A 70 kg person receives an absorbed dose of 2.0 mGy of gamma radiation. Calculate the energy absorbed.