Feb/March 2019

A wave has a frequency of $5\,\text{GHz}$. What is the time period of the wave?

Progressive waves

Two balls, with masses $m$ and $2m$, are moving in a vacuum with initial velocities $2v$ and $v$ respectively, and they collide head-on, as illustrated. Following the collision, the ball of mass $m$ rebounds leftwards with velocity $v$. What is the loss of kinetic energy in the collision?

Linear momentum and its conservation

A ball moves downward through a liquid at steady speed. Three forces act on it: upthrust, drag-force and weight. Which statement is correct?

Equilibrium of forces

A fairground ride has four carriages attached to a central vertical pole, as the plan view below shows. A motor turns the central pole about its axis, causing each of the four carriages to travel along a circular path. The distance from the centre of each carriage to the axis of the pole is $3.20\,\text{m}$. While moving, each carriage is acted on by an air resistance force of $85.0\,\text{N}$. Assume that no other significant resistive forces act. Which torque must the motor exert on the pole to maintain the system at constant maximum speed?

Turning effects of forces

A horizontal beam OX is uniform, is $4.0\,\text{m}$ in length and has a weight of $100\,\text{N}$. It is hinged to a wall at point O and held up by a cord XY that is fixed to the wall at Y. What is the tension in the cord?

Turning effects of forces

A hemisphere is placed so that its flat face is in contact with a table. It has radius $r$ and density $\rho$. The volume of a sphere is $\frac{4}{3}\pi r^3$. What is the mean pressure the object exerts on the table?

Density and pressure

Which statement most accurately describes the principle of conservation of energy?

Energy conservation

A crane is being used to raise containers from a ship. One container has a mass of $14\,000\,\text{kg}$ and is lifted straight up at a speed of $3.2\,\text{m s}^{-1}$. The electric motor providing the power to lift the container draws a current of $240\,\text{A}$ with a potential difference of $2200\,\text{V}$. What is the efficiency of the system?

Potential difference and power

The information below comes from a test carried out on a petrol engine in a motor car. power output: $150\,\text{kW}$ fuel consumption: $20$ litres per hour energy content of fuel: $40\,\text{MJ}$ per litre Determine the ratio $\dfrac{\text{power output}}{\text{power input}}$?

Energy conservation

Leonardo da Vinci suggested a flying machine that would operate in the manner of a screw, raising the pilot into the air. The pilot turns the ‘screw’. The combined mass of the machine and the pilot is $120\,\text{kg}$. What useful output power must the pilot supply to travel vertically upward at a steady speed of $2.5\,\text{m s}^{-1}$?

Gravitational potential energy and kinetic energy

A metal wire of length $l$ and cross-sectional area $A$ is secured at one end. When a mass $m$ is attached to the free end, the wire stretches by a distance $e$. What is an expression for the Young modulus $E$ of the metal?

Stress and strain

When the temperature is near $0\,\text{K}$, the specific heat capacity of a certain solid is described by $c = bT^3$, where $T$ denotes temperature and $b$ is a constant specific to the solid. The SI unit of specific heat capacity is $\text{J kg}^{-1}\text{K}^{-1}$. In SI base units, what is the unit of the constant $b$?

SI units

A spring has a spring constant of $6.0\,\text{N cm}^{-1}$. It is connected to a second spring with spring constant $4.0\,\text{N cm}^{-1}$. An $80\,\text{N}$ load is hung from the composite spring. What extension does this composite spring produce?

Elastic and plastic behaviour

The graph illustrates how the extension of a sample of a type of rubber changes as varying loads $F$ are applied and then slowly withdrawn. What is the best estimate of the strain energy in the rubber when a load of $80\,\text{N}$ is applied?

Elastic and plastic behaviour

A sound wave travels through air. The diagram shows the positions of the air molecules at one instant. Which distance is the same as the wavelength of the wave?

Transverse and longitudinal waves

In the upper row, the bars show a group of particles within the Earth that are stationary. In the lower row, the same particles are shown at a particular instant while a longitudinal wave moves through the Earth from left to right. What quantity should be measured in order to determine the amplitude of the particles’ oscillations in the lower row as the wave passes?

Transverse and longitudinal waves

A straight tube is sealed at one end, with a loudspeaker placed at the open end. The loudspeaker starts at a very low frequency and is then raised gradually. A sequence of loudness maxima is observed. The stationary wave that produces the first maximum has a node at the closed end and an antinode at the open end. The loudspeaker frequency is $f_1$ when the first maximum is observed. What is the loudspeaker frequency when the fourth maximum is observed?

Stationary waves

A buzzer that produces sound with frequency $846\ \text{Hz}$ is fixed to a string and whirled in a horizontal circle. Its linear speed is $25.0\ \text{m s}^{-1}$. The speed of sound is $340\ \text{m s}^{-1}$. What is the maximum frequency heard by the observer?

Doppler effect for sound waves

The diagram illustrates the main regions of the electromagnetic spectrum, and some details are labelled. It is not drawn to scale. What is a typical order of magnitude for the wavelength of the radiation in region Q?

Electromagnetic spectrum

P and Q are stationary points at the two ends of a string. A transverse stationary wave with a constant maximum amplitude is produced on the string. P, R and Q are the only positions on the string at which nodes occur. S and T are two points on the string, each at a distance $x$ from R. What is the relationship between points S and T?

Stationary waves

Two identical loudspeakers are linked in series to an a.c. supply, as illustrated. A microphone is then moved along the line PQ. Which graph best shows how the intensity of the sound detected by the microphone varies with distance from P?

Interference

A diffraction grating experiment is arranged with orange light of wavelength $600\ \text{nm}$. The grating has a slit separation of $2.00\ \mu\text{m}$. What is the angular separation $(\theta_2 - \theta_1)$ between the first-order and second-order maxima for the orange light?

The diffraction grating

An aircraft has a speed of $200\,\text{km h}^{-1}$ in still air. The wind is blowing from the west at $85.0\,\text{km h}^{-1}$. To travel due north, in what direction should the pilot point the aircraft?

Scalars and vectors

A pair of horizontal parallel plate conductors is spaced by 5.0\ \text{mm} in air. The lower plate is earthed, while the upper plate is at +50\ \text{V}. What is the electric field strength E at the midpoint between the plates?

Potential difference and power

The diagram illustrates the electric field close to a point charge, together with two electrons X and Y. Which row gives the forces on X and on Y?

Electric current

The electric current in a wire can be determined from the equation $I = Anvq$. Which statement is incorrect?

Electric current

As shown, three resistors are arranged in parallel across a power supply. The power dissipated in the resistors with resistances $2\,\Omega$, $3\,\Omega$ and $4\,\Omega$ is $P_2$, $P_3$ and $P_4$ respectively. What is the ratio $P_2 : P_3 : P_4$?

Potential difference and power

Which graph illustrates how the potential difference $V$ of a filament lamp varies with current $I$?

Resistance and resistivity

A wire with cross-sectional area $5.0 \times 10^{-6}\,\text{m}^2$ is constructed from a metal whose resistivity is $50 \times 10^{-8}\,\Omega\,\text{m}$. The potential difference across the wire is $6.0\,\text{V}$ and the current flowing through it is $3.0\,\text{A}$. What is the wire's length?

Resistance and resistivity

A cell with internal resistance $r$ and electromotive force (e.m.f.) $E$ is arranged in series with a resistor of resistance $R$. The resistance $R$ and the e.m.f. $E$ stay constant. The cell’s internal resistance $r$ varies with time. Which graph best represents how the current $I$ in the circuit changes with internal resistance $r$?

Practical circuits

Identical resistors are arranged in four combinations $P$, $Q$, $R$ and $S$ between terminals $X$ and $Y$. In descending order of combined resistance between $X$ and $Y$ (with the greatest first), what is the sequence?

Resistance and resistivity

The circuit diagram contains two resistors with resistances of $10\,\text{k}\Omega$ and $50\,\text{k}\Omega$, together with a component $Y$. A $6.0\,\text{V}$ power supply is applied. The electric potential of the lower wire is $0\,\text{V}$. The current in component $Y$ is negligible. What is the electric potential at junction $X$?

Potential dividers

A neutron $^1_0\text{n}$ strikes a $^{235}_{92}\text{U}$ nucleus and is taken in by it. The nucleus then fissions into nuclei of $^{141}_{56}\text{Ba}$ and $^{92}_{36}\text{Kr}$. How many neutrons are released when the $^{235}_{92}\text{U}$ nucleus splits?

Atoms, nuclei and radiation

A digital balance is used to measure ingredients in a laboratory. When a load is placed on the digital balance, an electronic circuit produces a current, which is then changed into a digital reading on the display. The electronic circuit produces a current of $2.0\,\text{mA}$ when a weight of $30\,\text{N}$ is applied, and a current of $0.5\,\text{mA}$ when a weight of $5\,\text{N}$ is applied. Which calibration curve might represent this circuit?

Practical circuits

Which word equation shows $\beta^+$ decay?

Atoms, nuclei and radiation

Four students measure a time interval whose true value is $1.734\,\text{s}$. Each student's reading is given below. Which reading is the most accurate?

Errors and uncertainties

A mass attached to the end of a spring moves up and down, as shown, after being released at time $t = 0$. Which graph indicates how the velocity changes with time?

Non-uniform motion

A stone is projected vertically upwards from a point $12\,\text{m}$ above the sea. After $3.4\,\text{s}$, it falls into the sea below. Air resistance is negligible. At what speed was the stone released when it was thrown?

Equations of motion

Two balls $X$ and $Y$ are travelling towards one another at speeds of $5\,\text{m s}^{-1}$ and $15\,\text{m s}^{-1}$ respectively. They undergo a perfectly elastic head-on collision, after which ball $Y$ moves to the right at a speed of $7\,\text{m s}^{-1}$. What is the speed and direction of ball $X$ after the collision?

Linear momentum and its conservation

If air resistance is ignored, a ball projected horizontally from a tower at velocity $v$ reaches the ground after $T$ seconds. However, when air resistance is included, which statement is correct?

Non-uniform motion

The ampere, metre and second are SI base units. State two more SI base units.

SI units

Define displacement.

Momentum and Newton's laws of motion

As shown in Fig. 3.1, balls X and Y travel over a horizontal frictionless surface. Ball X begins with velocity $3.0\,\text{m s}^{-1}$ along line AB. Ball Y has mass $2.5\,\text{kg}$ and starts with velocity $9.6\,\text{m s}^{-1}$ at an angle of $60^{\circ}$ to line AB. They collide at point B. After the collision, the two balls remain stuck together and move across the horizontal surface in a direction at right-angles to line AB, as shown in Fig. 3.2.

Linear momentum and its conservation

Define the term electric field strength.

Potential difference and power

Using two waves as your reference, state the principle of superposition.

Interference

Using energy changes, describe the electromotive force (e.m.f.) of a battery and the potential difference (p.d.) across a resistor. Describe: - e.m.f. - p.d.

Potential difference and power

The four particles listed below are: alpha, beta-plus, neutron, proton

Fundamental particles

What does gravitational potential at a point mean?

Gravitational potential

Fig. 10.1 shows a cross-section of a solenoid carrying current.

Electromagnetic induction

State the meaning of the term photon.

Photoelectric effect

One possible reaction occurring in the core of a nuclear reactor is represented by the incomplete nuclear equation below $^{235}_{92}\text{U} + ^{1}_{0}\text{n} \rightarrow ^{139}_{57}\text{La} + ^{95}_{42}\text{Mo} + 2^{1}_{0}\text{n} + \ldots$

Mass defect and nuclear binding energy

The pressure $p$ for an ideal gas with density $\rho$ is expressed by $p = \frac{1}{3}\rho\langle c^{2} \rangle$.

Kinetic theory of gases

A tube with a circular cross-section, closed at one end, has area $A$ and holds sand. The combined mass of the tube and the sand is $M$. As shown in Fig. 3.1, the tube floats vertically in a liquid of density $\rho$. It is pressed down a small distance into the liquid and then let go.

Simple harmonic oscillations

State three characteristics of a geostationary satellite’s orbit.

Kinematics of uniform circular motion

State the meaning of an electric field.

Electric field of a point charge

What is the capacitance of a parallel-plate capacitor?

Capacitors and capacitance

An ideal operational amplifier (op-amp) would have a voltage gain that remains constant and an infinite slew rate.

Characteristics of alternating currents

As shown in Fig. 8.1, a horseshoe magnet is resting on a top pan balance. A rigid copper wire is secured between the magnet’s poles, with the wire clamped at ends $A$ and $B$.

Force on a current-carrying conductor

Outline the principles behind computed tomography (CT) scanning.

Production and use of X-rays