Feb/March 2022

Which of the following could not represent a measurement of a physical quantity?

Physical quantities

An object of mass $2m$, moving through deep space with velocity $v$, breaks apart into two fragments of equal mass, with one fragment coming to rest. What is the kinetic energy of the fragment that is moving after the break-up?

Linear momentum and its conservation

A metal bar PQ lies horizontally and has a length of $50.0\,\text{cm}$; it is hinged at the end P. The diagram presents the bar as seen from above. At end Q, two forces, one of $16.0\,\text{N}$ and the other of $5.0\,\text{N}$, act in the horizontal plane, as indicated. What is the resultant moment about P caused by these two forces?

Turning effects of forces

A cube WXYZ with edge length $2.0\,\text{cm}$ and mass $24.0\,\text{g}$ is placed on a metre rule of negligible mass. The cube’s geometrical centre is directly above the $70.0\,\text{cm}$ mark on the scale of the rule. Because the cube is not of uniform density, its centre of gravity does not coincide with its geometrical centre. The cube’s centre of gravity lies in the plane of the diagram. The rule is supported by a pivot at the $50.0\,\text{cm}$ mark. A mass of $23.4\,\text{g}$ is positioned vertically above the $30.0\,\text{cm}$ mark. The rule remains horizontal and is in equilibrium. What can be inferred about the location of the cube’s centre of gravity?

Turning effects of forces

A rigid sphere is kept stationary on the seabed. Once the sphere is let go, it moves up to the surface of the sea. The seawater has a constant density. Which statement about the sphere, from the moment it is released until it reaches the surface, is correct?

Momentum and Newton's laws of motion

State one unit used for density.

Density and pressure

In a process, the total energy input $E_{\text{in}}$ is divided so that some is passed on as useful energy output $U$, while the remainder is passed on as wasted energy $W$. What is the efficiency of the process?

Energy conservation

An escalator has a length of $60\,\text{m}$ and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When no passengers are on it, the power needed to operate the escalator against friction is $2.0\,\text{kW}$. Passengers of mean mass $60\,\text{kg}$ use the escalator, and the power needed to overcome friction stays unchanged. What power is needed to run the escalator while it is carrying $20$ passengers and moving at $0.75\,\text{m s}^{-1}$?

Gravitational potential energy and kinetic energy

A rock with a mass of $40\,\text{kg}$ is dropped from rest at a point $20\,\text{m}$ above the surface of a planet. When the rock reaches the planet’s surface, its kinetic energy is $32\,\text{kJ}$. The planet has no atmosphere. What is the weight of the rock on the surface of the planet?

Gravitational potential energy and kinetic energy

A metal wire is pulled tight. The wire follows Hooke’s law. Which quantity has a value that remains constant?

Stress and strain

An object is pulled until it reaches the elastic limit. Which statement has to describe the stress in the object when it is at the elastic limit?

Elastic and plastic behaviour

A computer memory stick has a label showing a storage capacity of $128\ \text{GB}$. The letter B represents byte, which is a unit. What is the equivalent storage capacity?

SI units

Which statement concerning progressive waves is correct?

Progressive waves

A cathode-ray oscilloscope (CRO) is being used to find the frequency of a sound wave. The diagram displays the waveform on the screen. The time-base setting is $5.0\,\text{ms div}^{-1}$. What is the most accurate estimate of the sound wave’s frequency?

Progressive waves

An ambulance emits a warning signal at a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves at a constant velocity of $25\,\text{m s}^{-1}$ towards an observer. After it passes, it continues travelling away from the observer with the same velocity. What net change in the observed frequency occurs from the time when the ambulance is far behind the observer to the time when it is far in front of the observer?

Doppler effect for sound waves

At the same instant, the Sun emits short pulses of red, blue and green light. Each pulse covers the same distance on the way to Mars. Suppose the whole journey takes place through a vacuum. In what sequence would the pulses reach Mars?

Electromagnetic spectrum

Two coherent progressive waves arriving from separate sources overlap at one point. Which condition has to be met for the resultant amplitude to be zero at the point of overlap?

Interference

A corridor is $13.2\,\text{m}$ in length and has closed doors at both ends that reflect sound. The speed of sound in the air inside the corridor is $330\,\text{m s}^{-1}$. What is the lowest frequency of sound that could produce a stationary wave in the corridor with a node at the midpoint?

Stationary waves

Water waves with wavelength $\lambda$ are produced in a ripple tank. As they go through a narrow gap of width $d$ ($d$ is greater than $\lambda$), the waves are diffracted. Which combination of gap width and wavelength would produce the greatest reduction in the amount of diffraction?

Diffraction

Sound waves of wavelength $0.75\,\text{m}$ are produced in phase by two loudspeakers X and Y. As illustrated, an observer O can move to any position on a straight line through X and Y. O is located at a point where the waves arriving from X and Y are in phase. What could the distances OY and XY be?

Interference

Light with one wavelength is directed normally onto a diffraction grating. The diffraction pattern produced is shown on a screen. Which alteration would make the first-order intensity maxima lie farther apart on the screen?

The diffraction grating

For a wire that carries current, the current may be found using the equation shown. $I = Anvq$. What is the meaning of $n$?

Electric current

A man whose mass is $75.2\ \text{kg}$ measures his mass three times using a set of weighing scales. The readings he gets are: reading 1 = $80.2\ \text{kg}$, reading 2 = $80.1\ \text{kg}$, reading 3 = $80.2\ \text{kg}$. Which statement best describes the precision and accuracy of the weighing scales?

Errors and uncertainties

Over a period of $24$ hours, $6.0 \times 10^{23}$ free electrons pass one point in a wire. What is the wire’s average current?

Electric current

For the circuit diagram below, lamp P is rated $250\,\text{V},\,50\,\text{W}$ and lamp Q is rated $250\,\text{V},\,200\,\text{W}$. Both lamps are joined in series to a $250\,\text{V}$ power supply. Take the resistance of each lamp to be constant. Which statement most accurately describes what happens when the switch is closed?

Potential difference and power

A wire has a length of $0.80\,\text{m}$ and a diameter of $5.0 \times 10^{-4}\,\text{m}$. Its $I$-$V$ characteristic is shown. What is the resistivity of the metal that the wire is made from?

Resistance and resistivity

There are ten cells, and each has an electromotive force (e.m.f.) of $1.5\,\text{V}$, connected as shown. What is the total e.m.f. between terminals X and Y?

Practical circuits

A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is connected to a variable resistor, as illustrated. The resistance of the variable resistor is increased steadily from $r$ to $3r$. Which graph shows how the potential difference (p.d.) $v$ across the internal resistance varies with the p.d. $V$ across the variable resistor?

Potential difference and power

Kirchhoff’s two laws each assume that a particular quantity is conserved. Which row gives Kirchhoff’s first law and identifies the conserved quantity?

Kirchhoff's laws

A cell has an electromotive force (e.m.f.) of $8.0\,\text{V}$ and negligible internal resistance. It is included in a circuit, as shown. The reading $V_1$ is $4.0\,\text{V}$ and the reading $V_2$ is also $4.0\,\text{V}$. Calculate the resistance of resistor $R$.

Potential dividers

In the circuit diagram, the cells have negligible internal resistance and the galvanometer shows zero. What is the resistance of resistor $R$?

Kirchhoff's laws

When $\alpha$-particles are aimed at gold leaf: 1 nearly all $\alpha$-particles travel through with no deflection 2 a small number of $\alpha$-particles are turned through large angles. What explains these observations?

Atoms, nuclei and radiation

Nucleus X is radioactive and transforms into nucleus Y by decay. X and Y are isotopes of the same element. Which set of particles could have been released during the decay process?

Atoms, nuclei and radiation

Which of the following statements about scalar and vector quantities is correct?

Scalars and vectors

A meson with positive charge is made up of one quark and one antiquark. What might the quark and antiquark be?

Fundamental particles

How may the acceleration of an object be found?

Equations of motion

A sprinter records a time of $11.0\ \text{s}$ for a $100\ \text{m}$ race. At the start, she accelerates uniformly from rest until she reaches a speed of $10\ \text{m s}^{-1}$. After that, she continues at a constant speed of $10\ \text{m s}^{-1}$ up to the finish line. What is the sprinter’s uniform acceleration during the first part of the race?

Equations of motion

One horizontal force $F$ acts on block X, which is touching a separate block Y, as illustrated. The blocks stay in contact while they accelerate over a horizontal frictionless surface. Air resistance is negligible. X has a larger mass than Y. Which statement is correct?

Momentum and Newton's laws of motion

A car of mass $750\ \text{kg}$ is acted on by a horizontal driving force of $2.0\ \text{kN}$. It undergoes a forward horizontal acceleration of $2.0\ \text{m s}^{-2}$. What is the resistive force acting horizontally?

Momentum and Newton's laws of motion

An object is dropped from rest in a vacuum. The graph shows how the velocity $v$ of the object varies with time $t$. Which graph, on the same scales, shows the object falling through air?

Non-uniform motion

A sphere with radius $2.1\,\text{mm}$ descends through a liquid at terminal (constant) velocity, as illustrated in Fig. 1.1. Three forces act on the sphere while it is moving. Its weight is $7.2 \times 10^{-4}\,\text{N}$ and the upthrust on it is $4.8 \times 10^{-4}\,\text{N}$. The viscous force $F_v$ on the sphere obeys $F_v = krv$ where $r$ is the sphere’s radius, $v$ is its velocity and $k$ is a constant. The SI value of $k$ is $17$.

Momentum and Newton's laws of motion

At point $P$, water leaves the end of a hose pipe with a horizontal velocity of $6.6\,\text{m s}^{-1}$, as shown in Fig. 2.1. The point $P$ is at height $h$ above the ground, and the water lands at point $Q$. The horizontal separation between $P$ and $Q$ is $3.5\,$m. Air resistance is negligible. Between $P$ and $Q$, treat the water as a collection of non-interacting droplets, with only each droplet’s weight acting on it.

Equations of motion

A water jet strikes a vertical wall at right angles, as illustrated in Fig. 3.1. The water reaches the wall with a velocity of $5.0\,\text{m s}^{-1}$ in the horizontal direction. The jet has a cross-sectional area of $1.5 \times 10^{-4}\,\text{m}^2$. The density of the water is $1.0 \times 10^{3}\,\text{kg m}^{-3}$. After impact, the water flows down the wall.

Momentum and Newton's laws of motion

A child travels down a long slide, as illustrated in Fig. 4.1. The child begins from rest at the top X of the slide. While moving to the lower end Y, an average resistive force of $76\,\text{N}$ acts opposite to the child’s motion. At Y, the child’s kinetic energy is $300\,\text{J}$. The loss in gravitational potential energy of the child as it goes from X to Y is $3200\,\text{J}$.

Energy conservation

State the conditions needed for a stationary wave to be formed.

Doppler effect for sound waves

As illustrated in Fig. 6.1, the two ends of a metal resistance wire are attached to a battery with electromotive force (e.m.f.) $8.0\,\text{V}$ and negligible internal resistance. The resistance wire dissipates $36\,\text{W}$ of power.

Resistance and resistivity

A sodium-22 nucleus ($^{22}_{11}\text{Na}$) undergoes decay by releasing a $\beta^+$ particle. The decay produces a different nucleus.

Atoms, nuclei and radiation

The point $P$ in Fig. 1.1 is a point mass. On Fig. 1.1, sketch lines to show the gravitational field surrounding $P$.

Gravitational field of a point mass

Inside an X-ray tube, electrons are accelerated by a potential difference of $75\,\text{kV}$. They then collide with a tungsten target whose effective mass is $15\,\text{g}$. The electron energy is changed into the energy of X-ray photons with an efficiency of $5.0\%$. The remaining energy is turned into thermal energy.

Production and use of X-rays

Positron emission tomography (PET scanning) collects diagnostic data from a person, and that data is then used to construct an image.

PET scanning

State what luminosity of a star means.

Stellar radii

A fixed mass of ideal gas occupies volume $V$ and has pressure $p$. The gas then completes the cycle X to Y to Z to X, as shown in Fig. 2.1. Table 2.1 gives the values of $p$, $V$ and temperature $T$ for the gas at points X, Y and Z.

The first law of thermodynamics

A small wooden cuboid block of mass $m$ floats in water, as illustrated in Fig. 3.1. Its top face is horizontal and has area $A$. The density of the water is $\rho$.

Simple harmonic oscillations

State what an electric field line shows.

Electric potential

Figure 5.1 shows how the charge Q on one plate of a capacitor varies with potential difference V. In Fig. 5.2, the capacitor is connected to an 8.0\,\text{V} power supply together with two resistors R and S. R has resistance 25\,\text{k}\Omega and S has resistance 220\,\text{k}\Omega. The switch may be set to either position X or position Y.

Discharging a capacitor

A small solenoid with a cross-sectional area of $1.6 \times 10^{-3}\,\text{m}^2$ is located inside a larger solenoid with a cross-sectional area of $6.4 \times 10^{-3}\,\text{m}^2$, as shown in Fig. 6.1. The larger solenoid has $600$ turns and is connected to a d.c. power supply so that it produces a magnetic field. The smaller solenoid has $3000$ turns.

Electromagnetic induction

Alternating current (a.c.) is changed to direct current (d.c.) by means of a full-wave rectification circuit. Figure 7.1 shows one section of this circuit diagram.

Rectification and smoothing

State the equation for the de Broglie wavelength $\lambda$ of a particle in motion. State the meaning of any other symbol used.

Wave-particle duality

Polonium-211 ($^{211}_{84}\text{Po}$) undergoes alpha emission, forming a stable lead (Pb) isotope.

Radioactive decay