Feb/March 2018

Which unit has the same value as the coulomb?

SI units

Steel pellets, each having a mass of $0.60$ g, drop straight down onto a horizontal plate at a rate of $100$ pellets per minute. They arrive at the plate with a velocity of $5.0\,\text{m s}^{-1}$ and then bounce back with a velocity of $4.0\,\text{m s}^{-1}$. What is the average force exerted on the plate by the pellets?

Momentum and Newton's laws of motion

The diagram illustrates four forces acting on a circular object. Which row states the resultant force and resultant torque on the object?

Turning effects of forces

A charged oil drop remains at rest between two charged parallel plates. Which forces are acting on the oil drop?

Equilibrium of forces

For which example is the underlined body unable to be in equilibrium?

Equilibrium of forces

A car with mass $1100\,$kg is moving at a steady speed of $15\,\text{m s}^{-1}$ uphill on a slope inclined at $10^{\circ}$ to the horizontal. The total frictional forces on the car act down the slope and have a magnitude of $\dfrac{W}{5}$, where $W$ represents the car’s weight. What is the useful output power of the car’s engine?

Gravitational potential energy and kinetic energy

An older-style $60\,$W lamp changes $95\%$ of its energy supply into heat. A modern $4.0\,$W lamp produces the same light power output as the older lamp. What is the efficiency of the modern lamp?

Energy conservation

A bead starts from rest at point $P$ and moves along a wire, as shown. The track bends round to form a vertical circle with diameter $40\,\text{cm}$. At point $Q$, the bead’s speed is $1.4\,\text{m s}^{-1}$. Air resistance and friction on the wire are negligible. What is the height $h$ from which the bead is released?

Gravitational potential energy and kinetic energy

A small diesel engine consumes a volume of $1.5 \times 10^{4}\,\text{cm}^3$ of fuel per hour and delivers a useful power output of $40\,\text{kW}$. It may be assumed that $34\,\text{kJ}$ of energy is transferred to the engine when it uses $1.0\,\text{cm}^3$ of fuel. Determine the rate at which energy is transferred from the engine as wasted energy.

Energy conservation

Boxes $X$ and $Y$ each have the same mass. Box $X$ is raised straight up by a force of magnitude $F$ until it has moved through a height $h$. Box $Y$ is dragged up a slope by a force with the same magnitude so that it reaches the same height, as shown. Which statement is correct?

Gravitational potential energy and kinetic energy

A force-extension graph for a metal wire is shown. At which point on the graph does the metal wire cease to obey Hooke’s law?

Elastic and plastic behaviour

Which row gives a quantity and an incorrect unit?

SI units

The diagram depicts a large crane on a construction site raising a cube-shaped load at constant speed. A model of the crane, its load and the cable supporting the load is constructed. The material used for each component of the model is the same as that used for the full-size crane, cable and load. The model is one tenth full-size in every linear dimension. What is the ratio $\dfrac{\text{stress in the cable on the full-size crane}}{\text{stress in the cable on the model crane}}$?

Stress and strain

A wave pulse travels along a taut rope in the direction indicated. Which diagram represents how the displacement $s$ of particle $P$ in the rope changes with time $t$?

Progressive waves

A wave has period $T$, wavelength $\lambda$ and amplitude $A$. The wave is displayed on a graph of displacement $x$ plotted against distance $d$. Which graph is labelled correctly?

Progressive waves

The table gives possible orders of magnitude for the wavelengths of some of the main radiations in the electromagnetic spectrum. Which row gives the correct orders of magnitude for the wavelengths?

Electromagnetic spectrum

A vehicle is fitted with a microwave transmitter that produces microwaves at a fixed frequency. A stationary observer has a microwave receiver. The vehicle travels straight towards the observer at constant speed. The observer detects microwaves with frequency $F_o$. The vehicle then speeds up, while still moving towards the observer, continues at a larger constant speed for a period and then slows down until it comes to rest. How does the frequency of the microwaves detected by the observer change?

Doppler effect for sound waves

The diagram shows the display of an electromagnetic wave on a cathode-ray oscilloscope. The time base setting is $0.20\ \mu\text{s cm}^{-1}$. Which statement is correct?

Progressive waves

In a double-slit interference experiment, light with frequency $6.0 \times 10^{14}\ \text{Hz}$ falls on a pair of slits. On a screen placed some distance away, bright fringes spaced $3.0\ \text{mm}$ apart are seen. If the light frequency is altered to $5.0 \times 10^{14}\ \text{Hz}$, what is the new separation of the bright fringes?

Interference

Monochromatic light falls on two narrow slits separated by $0.1\ \text{mm}$. A pattern of bright and dark fringes appears on a screen $2.0\ \text{m}$ away. The spacing between neighbouring bright fringes is $8.0\ \text{mm}$. What path difference exists between the light waves from the two slits at the second order dark fringe?

Interference

A tube of length $L$ has both ends open. When a tuning fork oscillating at frequency $f_x$ is placed at one end, a stationary wave is produced in the tube. This is the lowest frequency of stationary wave that can exist in this tube. A second tube of length $2L$ has one end closed. When a tuning fork oscillating at frequency $f_y$ is held at the open end, a stationary wave is produced in this tube. This is the lowest frequency of stationary wave that can exist in this tube. Take the end correction for each tube to be negligible. Which equation is correct?

Stationary waves

Which statement describes a condition that allows diffraction to take place?

Diffraction

Two forces of the same size are shown by two coplanar vectors. One points east and the other points north. In which direction should a single force act to balance these two forces?

Equilibrium of forces

An electron moves into the region between two parallel plates that are $5.0\ \text{cm}$ apart and are kept at electric potentials of $+2000\ \text{V}$ and $-500\ \text{V}$, respectively. What is the electric force acting on the electron?

Potential difference and power

Which statement concerning electric charges in a uniform electric field is incorrect?

Potential difference and power

The diagram illustrates a simple circuit. Which statement is true?

Practical circuits

A resistor has resistance $R$. If the potential difference across the resistor is $V$, the current in the resistor is $I$. The power dissipated in the resistor is $P$. Work $W$ is done when charge $Q$ passes through the resistor. Which of the following is not a valid relationship between these variables?

Potential difference and power

A wire with a resistance of $9.55\ \Omega$ has a diameter measuring $0.280\ \text{mm}$. The wire is made from a metal whose resistivity is $4.90 \times 10^{-7}\ \Omega\ \text{m}$. Determine the wire's length.

Resistance and resistivity

Charge carriers, each carrying charge $q$, travel along a wire of fixed length. The number density of the charge carriers in the wire is $n$. What other information is needed, for this wire, to find the average drift velocity of the charge carriers in terms of $n$ and $q$?

Electric current

A potential divider circuit is set up using one variable resistor X and one fixed resistor Y, as illustrated. The potential difference across resistor X is $V_x$ and the potential difference of resistor Y is $V_y$. If the resistance of X is made larger, what change occurs in $V_x$ and in $V_y$?

Potential dividers

In the circuit shown, a cell with electromotive force (e.m.f.) $E$ and negligible internal resistance is connected. Since the voltmeter has a very high resistance, it measures a potential difference $V_{out}$. Determine the ratio $\dfrac{V_{out}}{E}$?

Potential dividers

Five resistors are arranged as shown. What is the combined resistance between points $P$ and $Q$?

Resistance and resistivity

A nucleus of neptunium-236 contains $93$ protons and $143$ neutrons. It decays by releasing an $\alpha$-particle. The nucleus produced then releases a $\beta^{-}$ particle. Which diagram shows how the number $P$ of protons and the number $N$ of neutrons change in these nuclei?

Atoms, nuclei and radiation

The density of paper is $800\,\text{kg m}^{-3}$. A standard sheet of paper measures $210\,\text{mm}$ in width and $300\,\text{mm}$ in length. A stack of $500$ sheets of paper is $50\,\text{mm}$ thick. What is the mass of one sheet of paper?

Density and pressure

A single neutron decays into a proton, a $\beta^{-}$ particle and an antineutrino. Which row shows the quark structure of the neutron and of the proton, together with the force responsible for this reaction?

Fundamental particles

Using the measurements shown, a person determines the potential difference across a wire. Which measured quantity makes the largest contribution to the percentage uncertainty in the calculated potential difference?

Errors and uncertainties

A cathode-ray oscilloscope (c.r.o.) is linked to an alternating voltage. The trace shown below appears on the screen. The oscilloscope time-base setting is $0.5\,\text{ms cm}^{-1}$ and the Y-plate sensitivity is $2\,\text{V cm}^{-1}$. Which statement about the alternating voltage is correct?

Practical circuits

A stone with mass $m$ is released from a tall building. Air resistance is significant. The acceleration of free fall is $g$. While the stone is moving with constant (terminal) velocity, which statement is correct?

Equilibrium of forces

A velocity-time graph for an object is shown. How may the object's total displacement be found?

Equations of motion

A girl throws a ball straight upwards. The ball takes $3.20\,$s to come back to her hand. Assume air resistance can be ignored. What is the initial speed at which the ball is thrown?

Equations of motion

Complete Fig. 1.1 by showing whether acceleration, speed, and power are vectors or scalars.

Equations of motion

Explain what the term work done means.

Gravitational potential energy and kinetic energy

In the deformation of a wire under tension, state what stress means.

Stress and strain

State the requirements for a stationary wave to be formed.

Stationary waves

State Kirchhoff’s second law.

Kirchhoff's laws

A sample of a radioactive isotope gives out a beam of $\beta^{-}$ radiation.

Atoms, nuclei and radiation

State what a line of force means in a gravitational field.

Gravitational field of a point mass

Define the term magnetic flux.

Electromagnetic induction

Fig. 11.1 shows some electron energy bands in a solid. The width of the forbidden band, together with the number density of charge carriers in each band, depends on the type of solid. Use band theory to explain why

Energy levels in atoms and line spectra

Suggest two reasons for the loss of sharpness in an X-ray image.

Production and use of X-rays

Define the radioactive decay constant.

Radioactive decay

Inside a cylinder there are $5.12\,\text{mol}$ of an ideal gas at pressure $5.60 \times 10^5\,\text{Pa}$ and volume $3.80 \times 10^4\,\text{cm}^3$.

The first law of thermodynamics

A mass is moving in simple harmonic motion with amplitude $x_0$. The greatest magnitude of the mass’s velocity is $v_0$. On Fig. 3.1, indicate how the velocity $v$ of the mass varies with displacement $x$.

Simple harmonic oscillations

Explain the meaning of the natural frequency of vibration of a system.

Damped and forced oscillations, resonance

Explain the key principles involved in using ultrasound to get diagnostic information about internal body structures.

Production and use of ultrasound

Fig. 6.1 can be used as a block diagram to show the digital transmission of speech.

Characteristics of alternating currents

State the meaning of electric potential at a point.

Electric potential

An ideal operational amplifier (op-amp) is described by infinite bandwidth and infinite slew rate. Explain what is meant by infinite bandwidth.

Rectification and smoothing

As shown in Fig. 9.1, a thin slab of conducting material has faces PQRS and VWXY set at right angles to a uniform magnetic field of flux density $B$. Electrons enter the slab perpendicular to face SRXY. A potential difference, called the Hall voltage $V_H$, forms across two faces of the slab.

Force on a moving charge