2022 HKDSE Physics Practice Paper | DSE Mock

A bar magnet is dropped vertically through a thick horizontal copper ring. Which of the following statements about the motion of the magnet is/are correct?\n\n(1) The acceleration of the magnet is always less than \(g\) during its fall.\n(2) The copper ring experiences a downward force when the magnet is entering and leaving.\n(3) If the copper ring has a small cut, the acceleration of the magnet is always equal to \(g\).

A rigid square conducting frame \(PQRS\) of side length \(a\) and mass \(m\) carries a steady current \(I\) clockwise. It is suspended from a spring scale in a region where a uniform horizontal magnetic field \(B\) exists, pointing into the paper, but only in the lower half of the frame (the upper side \(PQ\) is outside the magnetic field). What is the change in the reading of the spring scale if the direction of the current is reversed?

An ideal transformer has a primary coil of \(N_1\) turns and a secondary coil of \(N_2\) turns. A sinusoidal AC voltage \(V_{in} = V_0 \sin(\omega t)\) is applied to the primary. If both the angular frequency of the AC source (\(\omega \to 2\omega\)) and the number of turns in the primary coil (\(N_1 \to 2N_1\)) are doubled, while keeping \(V_0\) and \(N_2\) unchanged, how do the maximum secondary voltage \(V_{out, max}\) and the maximum magnetic flux \(\Phi_{max}\) in the core change?

Two identical light bulbs \(Y\) and \(Z\) are connected in parallel, and a switch \(S\) is connected in series with bulb \(Y\) in its branch. This parallel combination is connected in series with another identical bulb \(X\) across a DC voltage source of negligible internal resistance. When switch \(S\) is opened, what happens to the brightness of bulb \(X\) and bulb \(Z\)?

A battery of EMF \(\mathcal{E}\) and internal resistance \(r\) is connected to a variable resistor of resistance \(R\). A voltmeter of very high resistance is connected across the terminals of the battery. When \(R = 4\ \Omega\), the voltmeter reads \(8\text{ V}\). When \(R = 10\ \Omega\), the voltmeter reads \(10\text{ V}\). What are the EMF \(\mathcal{E}\) and the internal resistance \(r\) of the battery?

A rigid, thermally insulated container is divided into two compartments, A and B, of equal volume by a thin, thermally insulating partition. Compartment A contains \(1\text{ mol}\) of a monoatomic ideal gas at temperature \(T_0\). Compartment B contains \(2\text{ mol}\) of the same gas at temperature \(2T_0\). If the partition is removed and the gases mix and reach thermal equilibrium, what is the final temperature of the gas mixture?

The temperature of an ideal gas in a container of fixed volume is increased from \(27^\circ\text{C}\) to \(327^\circ\text{C}\). How do the root-mean-square speed of the gas molecules (\(v_{rms}\)) and the pressure of the gas (\(P\)) change?

A light ray is incident from medium X into medium Y. The angle of incidence is \(\theta_1\) and the angle of refraction is \(\theta_2\). If a graph of \(\sin\theta_2\) against \(\sin\theta_1\) is plotted, it is a straight line passing through the origin with a slope of \(0.75\).\n\nWhich of the following statements is/are correct?\n\n(1) Light travels faster in medium X than in medium Y.\n(2) Total internal reflection can occur when light travels from medium Y to medium X.\n(3) The critical angle for the interface between these two media is approximately \(48.6^\circ\).

In a double-slit experiment, monochromatic light of wavelength \(\lambda_1\) is used, and the fringe width on a screen at a distance \(D\) is measured to be \(w_1\). If the light source is replaced by another monochromatic light of wavelength \(\lambda_2\), and at the same time the slit separation is halved while the screen distance \(D\) remains unchanged, the new fringe width becomes \(3w_1\). What is the ratio \(\lambda_2 / \lambda_1\)?

A real object is placed in front of a thin converging lens of focal length \(f\). If the distance from the object to the lens is \(u\) and the magnification of the real image formed is \(m\), which of the following correctly describes the graph of \(1/m\) against \(u\)?

A square conducting loop of side length \(a = 0.1\text{ m}\) is moving with a constant velocity \(v = 2\text{ m s}^{-1}\) into a region of uniform magnetic field \(B = 0.5\text{ T}\) perpendicular to the loop's plane. The resistance of the loop is \(R = 0.2\ \Omega\). What is the magnitude of the external force required to keep the loop moving at this constant velocity while it is entering the magnetic field?

A copper rod of length \(L = 0.5\text{ m}\) is pivoted at one end and rotates with a constant angular speed \(\omega = 10\text{ rad s}^{-1}\) in a uniform magnetic field \(B = 0.2\text{ T}\) perpendicular to the plane of rotation. What is the induced electromotive force (e.m.f.) between the two ends of the rod?

A copper ring is placed horizontally. A bar magnet is released from rest from a position high above the ring and falls vertically along the central axis of the ring. Let \(a_1\) be the acceleration of the magnet when it is falling towards the ring from above, and \(a_2\) be its acceleration when it has passed through and is falling away from the ring. Neglecting air resistance, which of the following is correct?

A cell of constant electromotive force \(E\) and non-zero internal resistance \(r\) is connected to a variable resistor of resistance \(R\). As \(R\) is gradually increased from a very small value, how do the terminal voltage \(V\) across the cell and the power \(P\) dissipated in the variable resistor change?

A battery with internal resistance \(r = 2\ \Omega\) is connected to three external resistors: \(R_1 = 4\ \Omega\), \(R_2 = 6\ \Omega\), and \(R_3 = 12\ \Omega\). \(R_2\) and \(R_3\) are connected in parallel, and this parallel combination is connected in series with \(R_1\) across the terminals of the battery. If the power dissipated in \(R_1\) is \(16\text{ W}\), find the electromotive force (e.m.f.) of the battery.

A rigid container of fixed volume contains an ideal gas at a temperature of \(27^\circ\text{C}\) and a pressure of \(1.0 \times 10^5\text{ Pa}\). If half of the gas molecules are released from the container while the temperature of the remaining gas is raised to \(327^\circ\text{C}\) , what is the final pressure of the gas?

The molar mass of an ideal gas X is 4 times that of another ideal gas Y. If both gases are kept at the same temperature, what is the ratio of the root-mean-square speed of molecules of gas Y to that of gas X (i.e., \(v_{\text{rms, Y}} : v_{\text{rms, X}}\))?

A point light source is placed at the bottom of a tank filled with a liquid of refractive index \(n = 1.25\) to a depth of \(1.2\text{ m}\). An opaque circular disc is placed on the surface of the liquid with its center vertically above the light source. What is the minimum radius of the disc required to prevent any light from escaping through the surface of the liquid?

An object and a screen are placed \(90\text{ cm}\) apart. A thin converging lens of focal length \(f\) is placed between them. It is found that a sharp image can be formed on the screen at two different positions of the lens. If the distance between these two positions is \(30\text{ cm}\), find the focal length \(f\) of the lens.

In a Young's double-slit experiment, monochromatic light of wavelength \(\lambda\) is incident on two slits separated by a distance \(d\). The interference pattern is observed on a screen at a distance \(D\) from the slits. If the distance between the slits is halved and the distance from the slits to the screen is doubled, what must be the new wavelength of light used so that the fringe width remains unchanged?

A sealed cylinder with a frictionless piston contains a fixed mass of ideal gas. The cylinder is immersed in an ice-water bath. When the piston is slowly pushed inward by an external force, reducing the volume of the gas to half, which of the following statements is/are correct? (1) The average kinetic energy of the gas molecules increases. (2) The frequency of collisions of gas molecules on the cylinder wall increases. (3) The internal energy of the gas remains unchanged.

In the circuit shown, three identical light bulbs X, Y and Z are connected to a voltage source of negligible internal resistance. Bulb X is connected in series with a parallel combination of bulb Y and bulb Z. A switch S is connected in series with bulb Z in its branch. Initially, S is closed. What happens to the brightness of bulb X and bulb Y when the switch S is opened?

A rectangular conducting loop of wire is falling vertically under gravity through a region with a uniform horizontal magnetic field B directed into the page. The magnetic field exists only within a horizontal band of height H. The height of the loop is h (where h < H). Which of the following correctly describes the direction of the induced current in the loop (viewed from the front) as it enters, is fully inside, and leaves the magnetic field?

A ray of monochromatic light is incident normally on one of the shorter faces (legs) of a right-angled isosceles glass prism of refractive index n = 1.5. The ray then strikes the hypotenuse of the prism and emerges back into the air. What is the total angle of deviation of the light ray after it emerges from the prism?

A positive charge +q enters a region where a uniform electric field \(\vec{E}\) is directed along the +x direction and a uniform magnetic field \(\vec{B}\) is directed along the +y direction. At the instant the charge enters the region, its velocity \(\vec{v}\) is along the +z direction. Which of the following statements about the net electromagnetic force acting on the charge at this instant is correct?

Two identical rigid containers A and B contain ideal gases. Container A contains Helium gas (molar mass 4 g/mol) at temperature 300 K, and container B contains Oxygen gas (molar mass 32 g/mol) at temperature 600 K. What is the ratio of the root-mean-square (r.m.s.) speed of Helium molecules in A to that of Oxygen molecules in B?

A room's socket circuit is protected by a 13 A fuse. The operating voltage is 220 V. An air-conditioner rated '220 V, 2200 W' is connected to the circuit and is operating. Which of the following appliances can be switched on at the same time without blowing the fuse? (1) A computer rated '220 V, 350 W' and a ventilator rated '220 V, 100 W' (2) A vacuum cleaner rated '220 V, 800 W' (3) A television rated '220 V, 150 W' and a toaster rated '220 V, 500 W'

In a double-slit interference experiment, a red laser of wavelength 650 nm is incident on a double slit with a slit separation of d. Fringes with a width of w are observed on a screen at a distance D from the slits. If the red laser is replaced by a green laser of wavelength 520 nm, and the distance between the screen and the slits is increased to 1.5D, what is the new fringe width?

A copper ring with a small gap (slit) is released from rest and falls vertically over a vertically oriented bar magnet. Neglecting air resistance, which of the following statements is/are correct as the ring falls past the magnet? (1) An electromotive force (emf) is induced across the gap of the ring. (2) An induced current flows through the ring. (3) The acceleration of the ring is always equal to the acceleration due to gravity g.

A potential divider circuit consists of a light-dependent resistor (LDR) and a fixed resistor of resistance R connected in series across a constant 12 V d.c. supply. The output voltage \(V_{\text{out}}\) is measured across the LDR. When the LDR is in the dark, its resistance is 80 k\(\Omega\) and \(V_{\text{out}}\) is 8 V. When the LDR is exposed to bright light, its resistance decreases to 10 k\(\Omega\). What is the output voltage \(V_{\text{out}}\) under bright light?

A fixed mass of an ideal gas is kept in a cylinder with a frictionless piston. Initially, the absolute temperature of the gas is \(T\). The gas is then heated isobarically (at constant pressure) until its absolute temperature becomes \(1.5T\). Find the ratio of the final average translational kinetic energy of the gas molecules to the initial value, and the ratio of the final root-mean-square speed of the molecules to the initial value.

Three identical light bulbs, \(X\), \(Y\) and \(Z\), are connected to a DC source of constant e.m.f. and negligible internal resistance: bulb \(Y\) and bulb \(Z\) are connected in parallel, with a switch \(S\) in series with bulb \(Z\). This parallel combination is then connected in series with bulb \(X\) across the voltage source.

Initially, switch \(S\) is closed and all three bulbs are lit. If switch \(S\) is now opened, how does the brightness of bulb \(X\) and bulb \(Y\) change?

An outer circular loop and an inner circular loop are coplanar and concentric. The outer loop is connected to a variable DC voltage source such that a clockwise current \(I\) flows through it. If the current \(I\) in the outer loop is decreasing with time, what is the direction of the magnetic field at the common center and the direction of the induced current in the inner loop?

An ideal gas of volume \(2.0 \times 10^{-3} \text{ m}^3\) is trapped in a cylinder with a frictionless piston at a temperature of \(300 \text{ K}\) and a pressure of \(1.0 \times 10^5 \text{ Pa}\).

(a) The gas is heated at constant pressure until its volume doubles. Calculate the final temperature of the gas. (3 marks)

(b) The piston is then fixed in this new position, and the gas is cooled until its pressure drops to \(0.8 \times 10^5 \text{ Pa}\). Find the new temperature of the gas. (3 marks)

(c) State, with a brief reason, whether the internal energy of the gas increases, decreases, or remains unchanged after both processes. (2.4 marks)

A monochromatic light ray is incident normally on one of the shorter faces of a right-angled triangular glass prism of refractive index \(n = 1.50\). The acute angles of the prism are \(30^\circ\) and \(60^\circ\).

(a) Calculate the critical angle for the glass-air interface. (2.4 marks)

(b) Trace the path of the light ray as it enters, propagates through, and emerges from the prism. Calculate the angle of deviation of the ray as it exits the prism into air. (6 marks)

A rectangular metal frame of dimensions \(0.10 \text{ m} \times 0.20 \text{ m}\) and total resistance \(0.50 \Omega\) is pulled horizontally at a constant speed of \(4.0 \text{ m s}^{-1}\) out of a uniform magnetic field of \(0.80 \text{ T}\) directed perpendicularly into the page. The side of length \(0.20 \text{ m}\) is perpendicular to the direction of motion.

(a) Calculate the magnitude of the induced e.m.f. in the frame while it is exiting the field. (3 marks)

(b) Find the magnitude of the external force required to keep the frame moving at this constant speed. (3 marks)

(c) State the direction (clockwise or counter-clockwise) of the induced current and explain your answer using Lenz's Law. (2.4 marks)

Two long, straight parallel wires, \(X\) and \(Y\), are separated by a distance of \(0.15 \text{ m}\) in air. Wire \(X\) carries a current of \(6.0 \text{ A}\) upwards, and wire \(Y\) carries a current of \(4.0 \text{ A}\) downwards.

(a) Calculate the magnitude and state the direction of the magnetic field at a point \(P\) midway between the two wires. (4 marks)

(b) Determine the magnetic force per unit length acting on wire \(Y\) due to wire \(X\), and state whether this force is attractive or repulsive. (4.4 marks)

A battery of e.m.f. \(12.0 \text{ V}\) and internal resistance \(r = 1.50 \Omega\) is connected in series with a resistor \(R_1 = 4.50 \Omega\) and a parallel combination of two resistors, \(R_2 = 6.00 \Omega\) and \(R_3 = 3.00 \Omega\).

(a) Find the equivalent resistance of the external circuit. (2 marks)

(b) Calculate the terminal voltage of the battery. (3.4 marks)

(c) Calculate the electrical power dissipated in the resistor \(R_3\). (3 marks)

A glider \(A\) of mass \(0.40 \text{ kg\) travels at \(3.0 \text{ m s}^{-1}\) to the right on a frictionless air track and collides with a stationary glider \(B\) of mass \(0.20 \text{ kg}\). After the collision, glider \(B\) moves to the right at \(4.0 \text{ m s}^{-1}\).

(a) Calculate the velocity of glider \(A\) after the collision. (3 marks)

(b) Determine whether this collision is elastic, inelastic, or completely inelastic. Support your answer with calculations. (3 marks)

(c) Explain why the total momentum is conserved during the collision. (2.4 marks)

A box of mass \(15.0 \text{ kg}\) is pulled up a rough inclined plane of angle \(30^\circ\) by a constant force of \(120 \text{ N}\) parallel to the incline. The box starts from rest and moves a distance of \(8.00 \text{ m}\) along the incline. The coefficient of kinetic friction between the box and the incline is \(0.20\). (Take \(g = 9.81 \text{ m s}^{-2}\))

(a) Calculate the work done by the \(120 \text{ N}\) pulling force. (2 marks)

(b) Calculate the work done against friction. (3.4 marks)

(c) Calculate the final speed of the box at the end of the \(8.00 \text{ m}\) path. (3 marks)

A spacecraft of mass \(2.50 \times 10^3 \text{ kg}\) is in a circular orbit around Mars at an altitude of \(4.00 \times 10^6 \text{ m}\) above its surface. The mass of Mars is \(6.42 \times 10^{23} \text{ kg}\) and its radius is \(3.40 \times 10^6 \text{ m}\). (Take \(G = 6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}\))

(a) Calculate the orbital speed of the spacecraft. (4 marks)

(b) Calculate the period of the orbit in hours. (4.4 marks)

An electric heater rated at \(150 \text{ W}\) is used to heat \(0.45 \text{ kg}\) of an unknown liquid in a well-insulated container. The temperature of the liquid rises from \(22.0^\circ\text{C}\) to \(58.0^\circ\text{C}\) in \(4.00 \text{ minutes}\).

(a) Calculate the specific heat capacity of the liquid, assuming no heat is lost to the surroundings and the heat capacity of the container is negligible. (4 marks)

(b) In reality, the container absorbs some heat. If the container is made of aluminum of mass \(0.12 \text{ kg}\) and specific heat capacity \(900 \text{ J kg}^{-1} \text{ K}^{-1}\), calculate the corrected value of the specific heat capacity of the liquid. (4.4 marks)

A beaker of negligible heat capacity contains \(0.30 \text{ kg}\) of water at \(25.0^\circ\text{C}\). A piece of ice of mass \(0.08 \text{ kg}\) at \(0.0^\circ\text{C}\) is added to the water.

(Given: specific heat capacity of water = \(4200 \text{ J kg}^{-1} \text{ K}^{-1}\), specific latent heat of fusion of ice = \(3.34 \times 10^5 \text{ J kg}^{-1}\))

(a) Calculate the heat required to completely melt the ice at \(0.0^\circ\text{C}\). (2.4 marks)

(b) Determine whether all the ice will melt, and calculate the final temperature of the mixture when thermal equilibrium is reached. (6 marks)

Two main-sequence stars, \(S_1\) and \(S_2\), have masses \(M_1\) and \(M_2\) respectively, such that \(M_2 = 3 M_1\). Assuming that the luminosity \(L\) of a main-sequence star is related to its mass \(M\) by \(L \propto M^{3.5}\), what is the ratio of their main-sequence lifetimes \(\tau_1 / \tau_2\)?

A spectral line of a distant galaxy is observed at a wavelength of \(512.5\text{ nm}\). The laboratory wavelength of this spectral line is \(500.0\text{ nm}\). Using Hubble's constant \(H_0 = 75\text{ km s}^{-1}\text{ Mpc}^{-1}\) and speed of light \(c = 3.0 \times 10^5\text{ km s}^{-1}\), estimate the distance of the galaxy from Earth.

In a photoelectric effect experiment, when light of wavelength \(\lambda\) is shone on a metal plate, the stopping potential is \(V_0\). When light of wavelength \(\frac{\lambda}{2}\) is used, the stopping potential is \(2.5 V_0\). What is the work function of the metal?

In a hydrogen atom, an electron transitions from the \(n=4\) energy level to the \(n=2\) energy level, emitting a photon of energy \(E\). If an electron transitions from the \(n=3\) energy level to the \(n=1\) energy level, what is the energy of the emitted photon?

To reduce the Overall Thermal Transfer Value (OTTV) of a commercial building, which of the following measures is/are effective?
(1) Using double-glazed glass windows with a lower shading coefficient.
(2) Painting the external opaque walls with a lighter, more reflective color.
(3) Increasing the total area of the windows while keeping the total external wall area constant.

A wind turbine has blades of length \(L\). When the wind speed is \(v\), the electrical power output is \(P\) with an efficiency of \(\eta\). If the blade length is doubled, and the wind speed is halved while the efficiency remains unchanged, what is the new electrical power output?

A long-sighted person has a near point of \(80\text{ cm}\). What is the focal power (in dioptres) of the corrective lens required so that the person can read a book placed at a standard near point of \(25\text{ cm}\)?

An ultrasound pulse travels from muscle tissue into bone. The acoustic impedance of muscle is \(1.5 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\) and that of bone is \(6.0 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\). What percentage of the incident ultrasound intensity is reflected back into the muscle at the boundary?

A space probe is in a circular orbit around a spherical planet of mass \(M\) and radius \(R\). The height of the orbit above the planet's surface is \(h = R\). What is the ratio of the escape velocity from the planet's surface to the orbital speed of the probe?

An electron (mass \(m\), charge \(-e\)) and an alpha particle (mass \(4m\), charge \(+2e\)) are accelerated from rest through the same potential difference \(V\). What is the ratio of the de Broglie wavelength of the electron to that of the alpha particle?

A certain main sequence star has a luminosity that is 81 times that of the Sun. Assuming both stars can be modeled as blackbodies and the surface temperature of this star is twice that of the Sun, what is the ratio of the radius of this star \(R\) to the radius of the Sun \(R_\odot\)?

A distant galaxy has a redshift of \(z = 0.04\). According to Hubble's Law, what is the distance of this galaxy from Earth? (Take Hubble's constant \(H_0 = 70\text{ km s}^{-1}\text{ Mpc}^{-1}\) and the speed of light \(c = 3.0 \times 10^5\text{ km s}^{-1}\).)

A wind turbine has blades of length \(L\). Under a steady wind speed \(v\), it generates an electrical power \(P\) with an overall efficiency \(\eta\). If the blade length is increased to \(1.2 L\) and the wind speed increases to \(1.5 v\) while the overall efficiency remains unchanged, what is the new electrical power generated?

A room has a single-glazed glass window of area \(4.0\text{ m}^2\) and thickness \(3\text{ mm}\). The thermal conductivity of the glass is \(0.80\text{ W m}^{-1}\text{ K}^{-1}\). On a hot day, the outdoor temperature is \(35^\circ\text{C}\) and the indoor air-conditioned temperature is \(23^\circ\text{C}\). What is the rate of heat transfer through conduction through the window?

An X-ray beam of initial intensity \(I_0\) passes through a layer of soft tissue of thickness \(3.0\text{ cm}\) and then a layer of bone of thickness \(1.5\text{ cm}\). The linear attenuation coefficients of the soft tissue and bone for this X-ray energy are \(0.30\text{ cm}^{-1}\) and \(1.20\text{ cm}^{-1}\) respectively. What percentage of the initial intensity of the X-ray beam is transmitted?

When light of frequency \(f\) is shone on a metal surface, the maximum kinetic energy of the emitted photoelectrons is \(K\). When light of frequency \(1.5 f\) is shone on the same surface, the maximum kinetic energy becomes \(2K\). Find the work function of the metal in terms of \(h\) and \(f\).

A rooftop solar flat-plate collector of area \(3.0\text{ m}^2\) is used to heat domestic water. Solar radiation of intensity \(800\text{ W m}^{-2}\) is incident normally on the collector.

Water flows through the collector at a constant rate of \(0.040\text{ kg s}^{-1}\). The inlet temperature of the water is \(20^\circ\text{C}\) and the outlet temperature is \(31^\circ\text{C}\).
(Given: specific heat capacity of water \(c = 4200\text{ J kg}^{-1}\text{ }^\circ\text{C}^{-1}\))

(a) (i) Calculate the rate of solar energy falling on the collector. (2 marks)
(ii) Calculate the rate of heat energy absorbed by the water. (2 marks)
(iii) Hence, determine the efficiency of the solar collector. (2 marks)

(b) The collector features a transparent glass cover and a black-painted absorber plate. Briefly explain how this design minimizes heat loss to the surroundings via heat transfer mechanisms. (4 marks)

An ultrasound transducer is used to measure the thickness of a muscle layer in a patient's leg.

(a) Define the acoustic impedance \(Z\) of a medium and state its SI unit. (2 marks)

(b) The acoustic impedance of muscle is \(1.70 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\) and that of bone is \(7.80 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\). Calculate the fraction of ultrasound intensity reflected at the boundary between muscle and bone. (3 marks)

(c) An ultrasound pulse is transmitted into the leg. An A-scan display shows two prominent peaks. The first peak corresponds to the reflection at the fat-muscle boundary, and the second peak corresponds to the reflection at the muscle-bone boundary. The time interval between these two peaks on the oscilloscope is \(24.0\text{ }\mu\text{s}\).
If the speed of ultrasound in muscle is \(1540\text{ m s}^{-1}\), calculate the thickness of the muscle layer. (3 marks)

(d) Explain, with reference to acoustic impedance, why a coupling gel must be applied between the transducer and the patient's skin. (2 marks)