A Level Physics 9702 Paper 43, May/June 2023

Define gravitational field.

Define electric field.

State one similarity and one difference between the gravitational potential due to a point mass and the electric potential due to a point charge. similarity: ........................................................................................................................... ........................................................................................................................................... difference: .......................................................................................................................... ...........................................................................................................................................

An isolated uniform conducting sphere has mass $M$ and charge $Q$. The gravitational field strength at the surface of the sphere is $g$. The electric field strength at the surface of the sphere is $E$. Show that $$\frac{M}{Q}=\alpha \frac{g}{E}$$ where $\alpha$ is a constant.

Show that the numerical value of $\alpha$ is $1.35\times {10}^{20}{\text{ kg}}^2{\text{C}}^{-2}$.

Assume that the Earth is a uniform conducting sphere of mass $5.98\times {10}^{24}\text{ kg}$. The surface of the Earth carries a charge of $-4.80\times {10}^5\text{C}$ that is evenly distributed. Use the information in (b) to determine the electric field strength at the surface of the Earth. Give a unit with your answer. electric field strength = .................................. unit ...............

State how the direction of the electric field at the surface of the Earth compares with the direction of the gravitational field.

Explain, with reference to the forces acting on the sphere, why the length of the spring in Fig. 2.2 is greater than in Fig. 2.1.

The angle between the linear axis of the spring and the vertical is ${27}^{\circ }$. Show that the radius $r$ of the circle is $4.9\text{ cm}$.

Show that the tension in the spring is $3.2\text{ N}$.

The spring obeys Hooke’s law. Calculate the spring constant, in $\text{N}{\text{ cm}}^{-1}$, of the spring. spring constant = ............................................. $\text{N}{\text{ cm}}^{-1}$

Use the information in (b) to determine the centripetal acceleration of the sphere. centripetal acceleration = ................................................ $\text{m}{\text{ s}}^{-2}$

Calculate the period of the circular motion of the sphere. period = ...................................................... $\text{s}$

State the reason why two objects that are at the same temperature are described as being in thermal equilibrium.

Fig. 3.1 shows the variations with temperature of the densities of mercury and of water between $0^{\circ }\text{C}$ and ${100}^{\circ }\text{C}$. Temperature may be measured using the variation with temperature of the density of a liquid. Suggest why, for measuring temperature over this temperature range: mercury is a suitable liquid

Suggest why, for measuring temperature over this temperature range: water is not a suitable liquid.

A beaker contains a liquid of mass $120\text{ g}$. The liquid is supplied with thermal energy at a rate of $810\text{ W}$. The beaker has a mass of $42\text{ g}$ and a specific heat capacity of $0.84\text{ J}{\text{ g}}^{-1}{\text{K}}^{-1}$. The beaker and the liquid are in thermal equilibrium with each other at all times and are insulated from the surroundings. Fig. 3.2 shows the variation with time $t$ of the temperature of the liquid. State the boiling temperature, in ${}^{\circ }\text{C}$, of the liquid. temperature = .................................................... ${}^{\circ }\text{C}$

Determine the specific heat capacity, in $\text{J}{\text{ g}}^{-1}{\text{K}}^{-1}$, of the liquid. specific heat capacity = ........................................... $\text{J}{\text{ g}}^{-1}{\text{K}}^{-1}$

The experiment in (c) is repeated using water instead of the liquid in (c). The mass of liquid used, the power supplied, and the initial temperature are all unchanged. The specific heat capacity of water is approximately twice that of the liquid in (c). The boiling temperature of water is ${100}^{\circ }\text{C}$. On Fig. 3.2, sketch the variation with time $t$ of the temperature of the water between $t=0$ and $t=60\text{ s}$. Numerical calculations are not required.

State two of the basic assumptions of the kinetic theory of gases. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ...................................................................................................................................................

An ideal gas has amount of substance $n$. The gas is initially in state X, with pressure $2p$ and volume $V$. The gas is cooled at constant volume to state Y, with pressure $p$. The gas is then heated at constant pressure to state Z, with volume $2V$. Finally, the gas returns at constant temperature to state X. Determine an expression for the temperature $T$ of the gas in state X, in terms of $n$, $p$ and $V$. Identify any other symbols that you use.

On Fig. 4.1, sketch the variation with volume of pressure for the gas as the gas undergoes the three changes. The state X is labelled. Label states Y and Z.

During the change of state from Y to Z, the increase in internal energy of the gas is $U$. During the change of state from Z to X, the work done on the gas is $W$. Complete Table 4.1 to indicate, for each of the three changes of state, the increase in internal energy of the gas, the thermal energy transferred to the gas and the work done on the gas, in terms of $p$, $V$, $U$ and $W$. Table 4.1

A component is missing from the circuit of Fig. 5.1. Complete the circuit diagram in Fig. 5.1 by adding the circuit symbol for the missing component, correctly connected.

A capacitor C is shown in the circuit of Fig. 5.1. State the effect on $V_{\text{OUT}}$ of including the capacitor in the circuit.

Fig. 5.2 shows the variation with time $t$ of $V_{\text{IN}}$. Fig. 5.3 shows the variation with $t$ of $V_{\text{OUT}}$. Determine the frequency of $V_{\text{IN}}$. frequency = .................................................... Hz

Show that the time constant $\tau$ for the discharge of the capacitor through the resistor is $0.038\text{ s}$.

Calculate the capacitance of C. Give a unit with your answer. capacitance = .................................. unit ...............

The circuit of Fig. 5.1 is modified so that it produces full-wave rectification of an input voltage. Suggest, with a reason, how $V_{\text{OUT}}$ now varies with time when $V_{\text{IN}}$ is as shown in Fig. 5.2.

State what is meant by a magnetic field.

A long, straight wire P carries a current into the page, as shown in Fig. 6.1. On Fig. 6.1, draw four field lines to represent the magnetic field around wire P due to the current in the wire.

A second long, straight wire Q, carrying a current of $5.0\text{ A}$ out of the page, is placed parallel to wire P, as shown in Fig. 6.2. The flux density of the magnetic field at wire Q due to the current in wire P is $2.6\text{ mT}$. Calculate the magnetic force per unit length exerted on wire Q by wire P. force per unit length = ............................................... $\text{N}{\text{ m}}^{-1}$

State the direction of the force exerted on wire Q by wire P.

The flux density of the magnetic field at wire P due to the current in wire Q is $1.5\text{ mT}$. Determine the magnitude of the current in wire P. Explain your reasoning. current = ...................................................... A

State what is meant by the de Broglie wavelength.

Fig. 7.1 shows a glass tube in which electrons are accelerated through a high p.d. to form a beam that is incident on a thin graphite crystal. After passing through the graphite crystal, the electrons reach the fluorescent screen. The screen glows where the electrons strike it. Fig. 7.2 shows the fluorescent screen viewed end-on, from the right-hand side of Fig. 7.1. State the name of the phenomenon demonstrated by the pattern shown in Fig. 7.2.

Explain what can be concluded from the pattern in Fig. 7.2 about the nature of electrons.

The electrons in (b) are now accelerated through a greater potential difference between the cathode and the anode. On Fig. 7.3, sketch the pattern that is now seen on the fluorescent screen in Fig. 7.1.

Explain, with reference to de Broglie wavelength, the change in the pattern on the fluorescent screen.

Table 8.1 shows some data relating to the properties of air, gel and body tissue. The data are given to three significant figures. Table 8.1

Show that the specific acoustic impedance of gel is $1.68\times {10}^6\text{ kg}{\text{ m}}^{-2}{\text{ s}}^{-1}$.

Complete Table 8.1 by calculating the missing values to three significant figures. Use the space below for any working that you need.

Use the information in (a) to calculate the intensity reflection coefficient for: an air–tissue boundary intensity reflection coefficient = .........................................................

Use the information in (a) to calculate the intensity reflection coefficient for: a gel–tissue boundary. intensity reflection coefficient = .........................................................

Use your answers in (b) to explain why gel is applied to the skin during ultrasound scanning.

Define half-life.

A sample contains $N_0$ nuclei of carbon-11 and no other nuclei at time $t=0$. On Fig. 9.1, sketch the variation with $t$ of the number of nuclei of boron-11 in the sample.

Explain, with reference to the random nature of radioactive decay, why the activity of the carbon-11 sample in (b) decreases with time.

State, with reasons, whether a radiation detector placed near to the sample of carbon-11 indicates a measured count rate from the sample that is less than, the same as or greater than the activity of the sample.

State Hubble’s law. Identify any symbols that you use.

A star of luminosity $3.8\times {10}^{31}\text{ W}$ is a distance of $1.8\times {10}^{24}\text{ m}$ from the Earth. Calculate the radiant flux intensity at the Earth of the radiation emitted by the star. radiant flux intensity = .............................................. $\text{W}{\text{ m}}^{-2}$

The star in (b) is in a distant galaxy. A spectral line in the light from this galaxy is known to have a wavelength of $486\text{ nm}$. This spectral line in the light from the galaxy observed on the Earth has a wavelength of $492\text{ nm}$. Explain why the wavelength observed on the Earth is different from the wavelength that the galaxy is known to have emitted.

Determine a value for the Hubble constant $H_0$. $H_0$ = ................................................... ${\text{s}}^{-1}$