Feb/March 2021

What would be a sensible estimate of the density of sand?

Density and pressure

A firework initially at rest bursts into four fragments, each moving in a different direction within a horizontal plane. The diagram gives the velocity and mass of each fragment. What is the speed $v$ of fragment X?

Linear momentum and its conservation

A massive particle travels in a horizontal straight path through a uniform electric field in a vacuum, with the electric field acting vertically. The motion of the particle is affected significantly by gravity. What might be the direction of the electric field, and what sign, if any, does the charge on the particle have?

Equations of motion

A rod of length $5d$ is acted on by two parallel forces, each having magnitude $F$. Which diagram gives the locations of the two forces that produce the greatest torque on the rod?

Turning effects of forces

A mass of $30\,\text{kg}$ hangs from the lower end of a wire. A horizontal force $F$ acts on the mass so that it remains in equilibrium, while the wire makes an angle of $30^\circ$ to the vertical, as shown. What is the magnitude of $F$?

Equilibrium of forces

A balance is used to determine the mass $m$ of several cylindrical metal rods of length $l$. Each of the metal rods has the same radius $r$. The graph shows how $m$ varies with $l$. The gradient of the graph is $G$. Which expression gives the density of the metal?

Density and pressure

Two blocks $X$ and $Y$ rest on a horizontal frictionless surface. Block $Y$ has a greater mass than block $X$. A spring is attached to one end of block $Y$. The blocks are pressed together so that the spring is compressed between them, and they are kept stationary as illustrated. When they are released, the blocks travel in opposite directions. Which of the following statements is correct?

Linear momentum and its conservation

A gas is enclosed in a cylinder fitted with a movable piston. The cylinder has a circular cross-section with diameter $20.0\,\text{cm}$. The gas pressure is $102\,\text{Pa}$, and at the start the piston is $30.0\,\text{cm}$ above the cylinder base. When the gas is heated, the piston rises until it is $35.0\,\text{cm}$ above the base. Throughout this change, the pressure stays constant. What amount of work is done by the gas in moving the piston?

Energy conservation

An egg with a mass of $25\,\text{g}$ drops straight downward from the top of a table that is $900\,\text{mm}$ above the ground. Air resistance is negligible. Determine the kinetic energy of the egg when it reaches the ground.

Gravitational potential energy and kinetic energy

An aircraft moves with a constant velocity of $90\,\text{m s}^{-1}$ while flying horizontally. The diagram shows the horizontal forces acting on the aircraft. The mass of the aircraft is $2000\,\text{kg}$. Calculate the power generated by the thrust force.

Equilibrium of forces

Which expression gives the stress in a wire?

Stress and strain

What physical quantity could be expressed in units of $\text{N s}^2\,\text{m}^{-1}$?

SI units

A wire is pulled by applying successively larger forces $F$. For every force value used, the extension $x$ is measured. Using the collected data, a force-extension graph is drawn. Which statement concerning the area beneath the graph must be true?

Elastic and plastic behaviour

A progressive radio wave travelling in a vacuum has a frequency of $75\,\text{MHz}$. What phase difference exists between two points on the wave separated by $50\,\text{cm}$?

Progressive waves

Which statement is true for longitudinal waves but is not true for transverse waves?

Transverse and longitudinal waves

A loudspeaker producing a sound wave of one frequency is positioned a distance $L$ from a reflecting surface. A stationary wave forms with an antinode at the loudspeaker. A microphone is then moved from the loudspeaker towards the reflector. Before the microphone reaches the reflector, it detects four positions where the sound intensity is at a minimum. What is the wavelength of the sound wave?

Stationary waves

A source producing sound with frequency $F$ at point $Z$ is travelling at a constant speed. The arrangement of the emitted wavefronts is shown. Which row gives the sound frequencies detected by stationary observers at $X$ and $Y$?

Doppler effect for sound waves

What wavelength value is not possible for the named electromagnetic waves while they are travelling in a vacuum?

Electromagnetic spectrum

Waves P and Q arrive together at point X and superpose. At first, the two waves reach X in phase (zero phase difference), giving a resultant wave amplitude of $14.0\,\text{cm}$ at that point. The phase difference between the two waves is then altered so that, at X, they have a phase difference of $180^\circ$. The resultant wave now has an amplitude of $4.0\,\text{cm}$ at X. What is the amplitude of one wave at point X?

Interference

A water wave undergoes diffraction as it goes through the gap between two barriers in a ripple tank. As it travels through the gap, the wave is seen to ‘spread out’. Which two factors both influence the amount of diffraction seen?

Diffraction

Microwave sources P and Q emit coherent waves that have a phase difference of $180^\circ$. Both waves share the same wavelength $\lambda$. At point S, the interference pattern formed by waves from the two sources shows a minimum. The distance $(QS - PS)$ is known as the path difference. Which expression could represent the path difference?

Interference

A beam of red laser light with wavelength $633\,\text{nm}$ is incident normally on a diffraction grating having $600$ lines per mm. The red beam is then swapped for blue laser light of wavelength $445\,\text{nm}$. A new diffraction grating is selected so that the first-order maximum of the blue light is formed at the same point on the screen as the first-order maximum of the red light from the original laser. What is the number of lines per mm in the replacement diffraction grating?

The diffraction grating

A velocity vector is displayed. Its magnitude is $75\,\text{m s}^{-1}$ and it makes an angle of $30^\circ$ east of north. What are the components of the velocity vector in the northerly and in the easterly directions?

Scalars and vectors

Which diagram shows the field lines for the electric field generated by a pair consisting of one point positive charge and one point negative charge?

Scalars and vectors

The figure depicts a thundercloud with its base $500\,\text{m}$ above the ground. The potential difference between the cloud base and the ground is $200\,\text{MV}$. A raindrop carrying a charge of $4.0 \times 10^{-12}\,\text{C}$ is located in the region between the cloud and the ground. What is the electrical force acting on the raindrop?

Potential difference and power

The electric current $I$ in a metal wire is described by the equation $I = Anvq.$ What is represented by the symbol $n$?

Electric current

A cell with negligible internal resistance is joined to resistors $R_1$, $R_2$ and $R_3$, as illustrated. The cell supplies energy to the circuit and energy is lost in the resistors. Which word equation has to be correct?

Potential difference and power

A fixed resistor and a diode are joined in series to a battery with electromotive force (e.m.f.) $6.0\,\text{V}$ and negligible internal resistance. The graph shows how the current $I$ varies with potential difference (p.d.) $V$ for the diode. The current through the diode is $40\,\text{mA}$. What is the resistance of the fixed resistor?

Practical circuits

A electrical cable is made up of seven copper-wire strands, each with a diameter of $0.30\,\text{mm}$, linked in parallel. The resistivity of copper is $1.72 \times 10^{-8}\,\Omega\,\text{m}$. The current flowing in the cable is $13\,\text{A}$. What is the potential difference (p.d.) between two points on the cable separated by a distance of $1.0\,\text{m}$?

Resistance and resistivity

A cell with internal resistance is connected to switch $S$ and a variable resistor. A voltmeter is placed across the terminals of the cell, as shown. With switch $S$ open, the voltmeter gives a reading of $1.5\,\text{V}$. The switch is then closed and the variable resistor is set to a resistance of $4.0\,\Omega$. The voltmeter now shows $0.75\,\text{V}$. What is the internal resistance of the cell?

Practical circuits

A cell with electromotive force (e.m.f.) $E$ and negligible internal resistance is placed in a circuit, as illustrated. The voltmeter, which has a very high resistance, measures a potential difference $V_{out}$. What is the value of the ratio $\dfrac{V_{out}}{E}$?

Potential dividers

A battery is linked to a potentiometer. The potentiometer is made up of a uniform resistance wire and a sliding contact $P$. The potential difference (p.d.) $V$ between the sliding contact $P$ and the end $Q$ of the wire is found using a voltmeter. The sliding contact $P$ is then shifted from end $Q$ to end $R$ of the wire. Sliding contact $P$ is a distance $d$ from $Q$. Which graph represents how the p.d. $V$ changes with distance $d$?

Potential dividers

The diagram displays a section of the chart of nuclides, with neutron number on the vertical axis and proton number on the horizontal axis. An unstable nuclide $X$ undergoes decay by releasing an $\alpha$-particle. Which nuclide is produced when nuclide $X$ decays?

Atoms, nuclei and radiation

A micrometer screw gauge is used to find the diameter of a copper wire. The reading with the wire in place is shown in diagram 1. The wire is then taken out and the micrometer jaws are closed. The updated reading is shown in diagram 2. What is the diameter of the wire?

Errors and uncertainties

The nuclei for several common isotopes of hydrogen, helium, lithium and beryllium are displayed. Which nucleus has the same number of up quarks as down quarks?

Fundamental particles

A student records the current and the potential difference across a resistor in a circuit. current $= (50.00 \pm 0.01)\,\text{mA}$ potential difference $= (500.0 \pm 0.1)\,\text{mV}$ These readings are then used to find the resistance of the resistor. Determine the percentage uncertainty in the resistance value calculated.

Errors and uncertainties

Four cars, A, B, C and D, begin from rest and travel along a straight line. Each car takes the same time to increase its velocity to $60\,\text{km h}^{-1}$. Their velocity-time graphs are given. Which car reaches a velocity of $60\,\text{km h}^{-1}$ over the shortest distance?

Equations of motion

A cannon launches a cannonball with initial speed $v$ at an angle $\alpha$ above the horizontal. Which equation gives the maximum height $H$ attained?

Equations of motion

A ball of momentum $p$ hits a horizontal surface at an angle $\theta$ to the surface, as illustrated. It leaves the surface again with the same momentum magnitude, making an angle $\theta$ to the surface. The duration of contact between the ball and the surface is time $t$. What is the magnitude of the average resultant force acting on the ball during the collision?

Momentum and Newton's laws of motion

A skydiver, falling straight down through the air, opens his parachute. Which row gives the skydiver’s velocity immediately after the parachute opens?

Non-uniform motion

Write your answers in the spaces provided for every question.

Momentum and Newton's laws of motion

State the meaning of work done.

Energy conservation

A force stretches a spring. Figure 3.1 shows how the force $F$ varies with extension $x$.

Elastic and plastic behaviour

State what is meant by the principle of superposition.

Stationary waves

A sound source is tied to a rope and whirled round in a horizontal circle at constant speed, as shown in Fig. 5.1. The source has speed $12.0\,\text{m s}^{-1}$ and emits sound with frequency $951\,\text{Hz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. An observer, positioned very far from the source, hears the sound.

Doppler effect for sound waves

State Kirchhoff’s first law in words.

Kirchhoff's laws

The $\alpha$-particle scattering experiment results give evidence about atomic structure.

Atoms, nuclei and radiation

State the law of gravitation proposed by Newton.

Gravitational potential

The alternating power supply’s output p.d. is given by $V = 320\sin(100\pi t)$, where $V$ denotes the p.d. in volts and $t$ is measured in seconds.

Rectification and smoothing

A potential difference of $15\text{ kV}$ speeds up the electrons. They then strike a metal target, and an X-ray spectrum is emitted.

Production and use of X-rays

State what spontaneous decay means.

Radioactive decay

An ideal gas with a fixed mass is held at a temperature of $21\,^{\circ}\text{C}$. Its pressure is $2.3 \times 10^5\,\text{Pa}$ and its volume is $3.5 \times 10^{-3}\,\text{m}^3$.

Kinetic theory of gases

With a simple kinetic model of matter, describe the arrangement of particles in a solid.

Specific heat capacity and specific latent heat

The defining equation of simple harmonic motion is $a = -\omega^2 x$. State what the minus $(-)$ sign indicates in the equation.

Simple harmonic oscillations

State the meaning of amplitude modulation (AM) of a radio wave.

Characteristics of alternating currents

State one likeness between the gravitational field lines around a point mass and the electric field lines around a point charge.

Electric potential

Fig. 7.1 presents the circuit diagram, which includes an operational amplifier (op-amp).

Rectification and smoothing

Two long straight wires P and Q are arranged parallel to one another, as shown in Fig. 8.1. Each wire carries a current in the direction indicated. The magnetic field-line pattern in a plane perpendicular to wire P caused by the current in that wire is also shown.

Force on a current-carrying conductor

What does magnetic flux linkage mean?

Electromagnetic induction