2023 HKDSE Physics Practice Paper | DSE Mock

An electric heater of constant power is used to heat a substance of mass l. The substance is initially a solid at its melting point. It takes time \(t_1\) to melt completely into liquid, and then a further time \(t_2\) to raise the temperature of the liquid by \(\Delta T\). Find the ratio of the specific latent heat of fusion of the substance \(l_f\) to the specific heat capacity of its liquid state \(c_l\) (i.e., \(l_f / c_l\)).

A fixed mass of an ideal gas is kept in a rigid container of fixed volume. The temperature of the gas is increased from \(27^\circ\text{C}\) to \(327^\circ\text{C}\). Which of the following statements is/are correct?

(1) The average kinetic energy of the gas molecules is doubled.
(2) The root-mean-square speed of the gas molecules is doubled.
(3) The frequency of collisions between the gas molecules and the container walls is doubled.

A car is traveling along a straight horizontal road. At \(t=0\), the driver applies the brakes, causing the car to decelerate uniformly until it comes to rest at \(t = 2.5\text{ s}\). Let \(d_1\) be the distance traveled by the car from \(t=0\) to \(t=1\text{ s}\, and \)d_2\) be the distance traveled from \(t=1\text{ s}\) to \(t=2\text{ s}\). Find the ratio \(d_1 / d_2\).

Two blocks, \(A\) of mass \(m\) and \(B\) of mass \(3m\), are on a smooth horizontal surface. Initially, block \(B\) is at rest, and block \(A\) moves towards \(B\) with speed \(u\). After a head-on collision, block \(A\) rebounds with a speed of \(\frac{1}{5}u\). What is the total kinetic energy of the system after the collision?

A block of mass \(m\) is released from rest from the top of a rough inclined plane of inclination \(\theta\). The block slides down the plane for a distance \(L\) and reaches a speed \(v\) at the bottom. What is the average power developed by the friction force on the block during this motion?

A ray of light is incident from medium X into medium Y. The critical angle for total internal reflection at the boundary is \(\theta_c\). If the speed of light in medium X is \(v\), what is the speed of light in medium Y?

Two coherent wave sources \(S_1\) and \(S_2\) vibrate in phase and produce waves of wavelength \(\lambda\). At point \(P\), constructive interference is observed, with a path difference of \(|S_1 P - S_2 P| = 2\lambda\). If the frequency of both sources is now increased by \(25\%\) while the wave speed remains unchanged, which of the following describes the interference at point \(P\)?

A battery of e.m.f. \(\mathcal{E}\) and internal resistance \(r\) is connected to a variable resistor of resistance \(R\). When \(R = 2\,\Omega\), the current in the circuit is \(1.2\text{ A}\). When \(R = 5\,\Omega\), the current in the circuit is \(0.6\text{ A}\). Find the e.m.f. \(\mathcal{E}\) and the internal resistance \(r\) of the battery.

A circular metal ring is dropped horizontally from rest, passing through a region with a uniform magnetic field directed vertically downwards. The magnetic field exists only within a horizontal layer of a certain thickness, which is larger than the diameter of the ring. What are the directions of the induced current in the ring (viewed from above) as it enters and leaves the magnetic field region?

Two point charges, \(+Q\) and \(-4Q\), are fixed at points \(A\) and \(B\) respectively, separated by a distance \(d\) in vacuum. At which of the following positions is the net electric field strength due to these two charges equal to zero?

A solid substance of mass \(0.2\text{ kg}\) is heated by a heater of power \(50\text{ W}\). The temperature-time graph of the substance shows that its temperature increases from \(20^\circ\text{C}\) to \(50^\circ\text{C}\) in the first 2 minutes, and then remains constant at \(50^\circ\text{C}\) for the next 5 minutes to melt completely. Find the specific latent heat of fusion of the substance.

A car accelerates from rest along a straight road. The displacement-time graph of the car is a parabola for the first \(4\text{ s}\), and then becomes a straight line afterwards. The car travels a total distance of \(48\text{ m}\) in the first \(6\text{ s}\). Find the acceleration of the car during the first \(4\text{ s}\).

Two blocks \(A\) (mass \(m\)) and \(B\) (mass \(3m\)) are on a smooth horizontal surface. Block \(A\) moves with speed \(v\) towards block \(B\) which is at rest. After they collide, block \(A\) bounces back with speed \(v/5\). What fraction of the initial kinetic energy of the system is lost in the collision?

A light ray enters a semi-circular glass block of refractive index \(n = 1.5\) from air. Inside the glass, it strikes the flat surface of the block at the center of the semicircle at an angle of incidence \(\theta\). If the reflected ray and refracted ray are perpendicular to each other, find the value of \(\theta\).

A stationary wave is formed on a stretched string of fixed length. When vibrating in its third harmonic, the frequency is \(240\text{ Hz}\). If the tension in the string is quadrupled, what is the fundamental frequency of the string?

Two small identical conducting spheres \(X\) and \(Y\) carry charges of \(+6\mu\text{C}\) and \(-2\mu\text{C}\) respectively, and are separated by a distance \(r\). The electrostatic force between them is \(F\) (attractive). If they are brought into contact and then separated back to the same distance \(r\), what is the new electrostatic force between them?

A circuit consists of a real battery of electromotive force \(\varepsilon\) and internal resistance \(r\), connected in series with a variable resistor \(R\). As the resistance of \(R\) is increased, how do the terminal potential difference across the battery \(V\) and the power dissipated in the internal resistance \(P_{\text{int}}\) change?

A block of mass \(m\) is sliding down a rough inclined plane at a constant velocity. The inclined plane makes an angle \(\theta\) with the horizontal. What is the magnitude of the net force exerted by the inclined plane on the block?

A square conducting loop of side length \(L\) and resistance \(R\) is pulled at a constant speed \(v\) out of a region of uniform magnetic field \(B\) (directed perpendicularly into the page). What is the external force required to keep the loop moving at this constant speed?

An electric motor is used to lift a water bucket of mass \(10\text{ kg}\) vertically upwards. The bucket starts from rest and accelerates uniformly to a speed of \(2\text{ m s}^{-1}\) in \(2\text{ s}\). Take \(g = 9.81\text{ m s}^{-2}\). What is the average useful output power of the motor during these \(2\text{ s}\)?

A gas cylinder has a safety valve that opens when the pressure inside exceeds \(3.0 \times 10^5 \text{ Pa}\). Initially, the cylinder contains an ideal gas at a pressure of \(1.2 \times 10^5 \text{ Pa}\) and a temperature of \(27^\circ\text{C}\). Assuming the volume of the cylinder remains constant, what is the temperature at which the safety valve will open?

Two smooth blocks \(A\) and \(B\) of masses \(m\) and \(3m\) respectively are on a smooth horizontal surface. Block \(A\) moves towards block \(B\) (which is initially at rest) with speed \(v\). If they collide head-on and elastically, what are the velocities of \(A\) and \(B\) immediately after the collision? (Take the initial direction of motion of \(A\) as positive)

In a double-slit interference experiment using monochromatic light, the fringe width on a screen is \(\Delta y\). If the slit separation is doubled and the distance between the slits and the screen is halved, what is the new fringe width?

A bar magnet is dropped vertically through the center of a horizontal copper ring. Which of the following statements about this process is/are correct? (1) Before passing through the ring, the magnet falls with an acceleration less than \(g\). (2) The induced current in the ring reverses its direction as the magnet passes through the center of the ring. (3) The copper ring experiences a downward force while the magnet is falling above the ring.

A student mixes \(2.0 \text{ kg}\) of water at \(80^\circ\text{C}\) with \(3.0 \text{ kg}\) of a liquid \(X\) at \(20^\circ\text{C}\) in a well-insulated container. The final steady temperature of the mixture is \(50^\circ\text{C}\). What is the specific heat capacity of liquid \(X\)? (Given: specific heat capacity of water = \(4200 \text{ J kg}^{-1} \text{K}^{-1}\))

A car of mass \(1200 \text{ kg}\) travels up a slope inclined at \(\theta\) to the horizontal, where \(\sin \theta = 0.1\). The total resistive force opposing the motion is constant at \(400 \text{ N}\). If the car's engine operates at a constant power of \(40 \text{ kW}\), what is the maximum steady speed of the car up the slope? (Take \(g = 10 \text{ m s}^{-2}\))

A resonance tube closed at one end is filled with air. A tuning fork of frequency \(512 \text{ Hz}\) is held near the open end of the tube. The first resonance occurs when the length of the air column is \(16.0 \text{ cm}\). Assuming the end correction is negligible, what is the length of the air column when the next resonance occurs?

Three identical resistors, each of resistance \(R\), are connected to a cell of negligible internal resistance. Two of the resistors are connected in parallel, and this combination is connected in series with the third resistor. If the total electrical power dissipated in the entire circuit is \(P\), what is the power dissipated in the third resistor?

A radioactive sample initially contains \(N_0\) active nuclei of isotope \(X\) and \(2N_0\) active nuclei of isotope \(Y\). The half-life of \(X\) is \(12 \text{ hours}\) and the half-life of \(Y\) is \(4 \text{ hours}\). After how many hours will the number of active nuclei of \(X\) and \(Y\) in the sample be equal?

Two artificial satellites \(A\) and \(B\) orbit the Earth in circular orbits of radii \(R\) and \(4R\) respectively. If the orbital speed of satellite \(A\) is \(v\), what is the orbital speed of satellite \(B\)?

Ball A is projected horizontally with speed \(u\) from the top of a vertical tower of height \(H\). At the same instant, ball B is projected vertically upwards with speed \(v\) from the ground at a horizontal distance \(D\) from the foot of the tower. If the two balls collide in mid-air, which of the following expressions is correct? (Neglect air resistance.)

A solid substance is heated from \(20^\circ\text{C}\) by a heater of constant power. The temperature of the substance increases steadily to its melting point of \(80^\circ\text{C}\) in \(4\text{ minutes}\). It then remains at \(80^\circ\text{C}\) for \(6\text{ minutes}\) until it melts completely. Find the ratio of the specific latent heat of fusion \(\ell_f\) to the specific heat capacity of the solid state \(c_s\) of this substance.

A rigid, triangular conducting loop (in the shape of an isosceles right-angled triangle) enters a region of uniform magnetic field at a constant velocity \(v\) directed parallel to one of its shorter sides. One of its acute-angled vertices enters the field first at time \(t=0\). Before the loop is completely inside the magnetic field, how does the magnitude of the induced electromotive force (e.m.f.) \(\varepsilon\) in the loop vary with time \(t\)?

A toy car starts from rest and moves along a straight line. It first accelerates uniformly for \(t_1\) seconds, then travels at a constant maximum velocity \(v_{\max}\) for \(6\text{ s}\), and finally decelerates uniformly to rest for another \(t_1\) seconds. The total time taken for the whole journey is \(15\text{ s}\) and the total distance traveled is \(120\text{ m}\).

(a) Sketch the velocity-time (\(v\)-\(t\)) graph of the toy car. (2 marks)
(b) Determine the value of \(t_1\) and find the maximum velocity \(v_{\max}\). (4 marks)
(c) Calculate the magnitude of the acceleration of the toy car. (3.33 marks)

Ball A of mass \(0.5\text{ kg}\) moving at \(4.0\text{ m s}^{-1}\) along a frictionless horizontal floor collides head-on with Ball B of mass \(0.3\text{ kg}\) which is initially at rest. The collision is perfectly elastic.

(a) State the principles of conservation of linear momentum and conservation of kinetic energy as applied to this collision. (2 marks)
(b) Calculate the velocities of Ball A and Ball B after the collision. (5.33 marks)
(c) If the duration of the collision is \(0.05\text{ s}\), calculate the average force exerted on Ball B during the collision. (2 marks)

A small ball is projected horizontally from the top of a vertical cliff of height \(45.0\text{ m}\) with an initial horizontal speed of \(20.0\text{ m s}^{-1}\). Air resistance is negligible. (Take \(g = 9.81\text{ m s}^{-2}\))

(a) Show that the time of flight of the ball before hitting the ground is approximately \(3.03\text{ s}\). (2.33 marks)
(b) Calculate the horizontal distance from the base of the cliff to the point where the ball lands. (3 marks)
(c) Determine the speed of the ball and the angle its velocity vector makes with the horizontal just before it hits the ground. (4 marks)

An ideal gas is sealed in a cylinder fitted with a frictionless piston. Initially, the gas volume is \(2.0 \times 10^{-3}\text{ m}^3\), its temperature is \(300\text{ K}\), and its pressure is \(1.0 \times 10^5\text{ Pa}\).

(a) The gas is first heated while the piston is locked in position (constant volume) until its temperature reaches \(450\text{ K}\). Calculate the new pressure of the gas. (3 marks)
(b) The piston is then unlocked, and the gas is allowed to expand at a constant pressure of \(1.5 \times 10^5\text{ Pa}\) until its volume reaches \(3.0 \times 10^{-3}\text{ m}^3\).
(i) Calculate the final temperature of the gas. (3 marks)
(ii) Explain, in terms of molecular kinetic theory, why the pressure would decrease if the gas volume was increased while the temperature was kept constant. (3.33 marks)

A ray of monochromatic light is incident from air onto the flat face of a semi-circular glass block of refractive index \(n = 1.52\).

(a) Calculate the critical angle \(c\) for the glass-air interface. (3 marks)
(b) The light ray enters the block at the center of the flat face from air with an angle of incidence of \(45.0^\circ\). Calculate the angle of refraction \(r\) inside the glass block. (3.33 marks)
(c) Describe the path of this ray as it exits the curved boundary of the semi-circular glass block back into the air. Explain your answer. (3 marks)

In a Young's double-slit experiment, monochromatic red light of wavelength \(\lambda = 650\text{ nm}\) is used. The slit separation is \(d = 0.25\text{ mm}\) and the screen is placed at a distance \(D = 1.80\text{ m}\) from the slits.

(a) Calculate the fringe width (separation between adjacent bright fringes) observed on the screen. (3.33 marks)
(b) State and explain how the fringe width would change if:
(i) The red light is replaced by green light of wavelength \(530\text{ nm}\). (3 marks)
(ii) The distance between the slits and the screen is doubled. (3 marks)

Two point charges, \(Q_1 = +4.0\text{ }\mu\text{C}\) and \(Q_2 = -9.0\text{ }\mu\text{C}\), are fixed on the x-axis at \(x = 0\) and \(x = 0.30\text{ m}\) respectively.
(Take \(k = 8.99 \times 10^9\text{ N m}^2\text{ C}^{-2}\))

(a) Calculate the magnitude and state the direction of the electrostatic force exerted on \(Q_1\) by \(Q_2\). (3.33 marks)
(b) Determine the coordinate on the x-axis where the net electric field due to these two charges is zero. (6 marks)

A real battery has an electromotive force (e.m.f.) of \(\mathcal{E} = 12.0\text{ V}\) and an internal resistance of \(r = 1.0\text{ }\Omega\). It is connected to an external circuit consisting of two resistors, \(R_1 = 6.0\text{ }\Omega\) and \(R_2 = 3.0\text{ }\Omega\), connected in parallel, which are in series with a third resistor, \(R_3 = 5.0\text{ }\Omega\).

(a) Calculate the equivalent resistance of the parallel combination of \(R_1\) and \(R_2\). (2 marks)
(b) Calculate the total current flowing through the battery. (3.33 marks)
(c) Determine the terminal voltage of the battery and the current flowing through resistor \(R_1\). (4 marks)

A flat square coil of side length \(s = 0.10\text{ m}\) with \(N = 50\) turns of wire is pulled at a constant speed of \(v = 2.0\text{ m s}^{-1}\) into a region of uniform magnetic field of flux density \(B = 0.40\text{ T}\). The magnetic field is perpendicular to the plane of the coil and points directly into the page.

(a) State Faraday's Law of Electromagnetic Induction. (2 marks)
(b) Calculate the magnetic flux through a single turn of the coil when it is completely inside the magnetic field region. (2.33 marks)
(c) Calculate the magnitude of the induced electromotive force (e.m.f.) in the coil as it enters the magnetic field. (3 marks)
(d) Use Lenz's Law to determine whether the induced current flows in a clockwise or counter-clockwise direction as the coil enters the field. Explain your reasoning. (2 marks)

Two stars, A and B, form a binary star system orbiting around their common centre of mass. The mass of star A is twice that of star B. If the orbital period of star A is \(T\), what is the orbital period of star B, and what is the ratio of their orbital radii \(r_A / r_B\)?

Two stars, X and Y, have the same apparent magnitude. The parallax of star X is \(0.05\text{ arcseconds}\), and that of star Y is \(0.01\text{ arcseconds}\). If star X has a surface temperature of \(6000\text{ K}\) and star Y has a surface temperature of \(3000\text{ K}\), find the ratio of their radii \(\frac{R_X}{R_Y}\).

A distant galaxy has a hydrogen spectral line (rest wavelength \(\lambda_0 = 656.3\text{ nm}\)) redshifted to \(\lambda = 678.0\text{ nm}\). If the Hubble constant is \(70\text{ km s}^{-1}\text{ Mpc}^{-1}\), estimate the distance of the galaxy from Earth. (Take speed of light \(c = 3.0 \times 10^5\text{ km s}^{-1}\))

When monochromatic light of frequency \(f\) shines on a metal surface, the stopping potential of the emitted photoelectrons is \(V_1\). When the frequency of the light is increased to \(1.5f\), the stopping potential becomes \(V_2\). What is the threshold frequency of the metal?

An electron and an \(\alpha\)-particle are accelerated from rest through the same potential difference. What is the ratio of the de Broglie wavelength of the electron (\(\lambda_e\)) to that of the \(\alpha\)-particle (\(\lambda_\alpha\))? (Assume the mass of an \(\alpha\)-particle is \(7300\) times that of an electron, and the charge of an \(\alpha\)-particle is twice that of an electron.)

According to Bohr's model of the hydrogen atom, the orbital radius of the electron in the ground state (\(n=1\)) is \(a_0\). What is the de Broglie wavelength of the electron in the second excited state (\(n=3\))?

A solar panel of area \(2.5\text{ m}^2\) is installed on a rooftop. The average solar intensity (irradiance) normal to the panel is \(800\text{ W m}^{-2}\). The panel is used to charge a \(12\text{ V}\) battery. If the panel charges the battery with a steady current of \(8.0\text{ A}\) under this sunlight, what is the efficiency of the solar panel system?

An air-conditioner has a cooling capacity of \(3.5\text{ kW}\) and a Coefficient of Performance (COP) of \(2.8\). If it operates for \(8.0\text{ hours}\) a day, how much electrical energy (in \(\text{kWh}\)) does it consume in a day?

A short-sighted person has a far point of \(50\text{ cm}\). What are the focal length and power of the contact lens required to enable this person to see distant objects clearly?

The linear attenuation coefficient of a certain tissue for \(100\text{ keV}\) X-rays is \(0.35\text{ cm}^{-1}\). What percentage of the initial intensity of the X-ray beam is transmitted through a \(4.0\text{ cm}\) thick layer of this tissue?

Star A and Star B are two stars. The luminosity of Star A is 64 times that of Star B, and the surface temperature of Star A is twice that of Star B. Find the ratio of the radius of Star A to that of Star B, \(R_A : R_B\).

A satellite is in a stable circular orbit of radius \(r\) around the Earth with an orbital speed \(v\). If the orbit radius is adjusted to \(1.44r\), what is the new orbital speed of the satellite?

In a photoelectric effect experiment, light of wavelength \(\lambda\) is incident on a metal surface, and the measured stopping potential is \(V_s\). If the wavelength of the incident light is decreased to \(\frac{\lambda}{2}\), the new stopping potential \(V_s'\) will satisfy which of the following relations?

An electron and a proton are accelerated from rest through the same potential difference. Given that the mass of a proton is 1840 times the mass of an electron, find the ratio of the de Broglie wavelength of the electron to that of the proton.

A solar panel with an area of \(2.0 \text{ m}^2\) is exposed to solar radiation of intensity \(800 \text{ W m}^{-2}\). The efficiency of the solar panel in converting solar energy to electricity is \(15\%\). How many hours of such solar radiation are required to fully charge a completely discharged \(12\text{ V}, 80\text{ Ah}\) battery?

An ultrasound wave is incident normally on the boundary between muscle and bone. The acoustic impedance of muscle is \(1.70 \times 10^6 \text{ kg m}^{-2} \text{ s}^{-1}\) and that of bone is \(7.80 \times 10^6 \text{ kg m}^{-2} \text{ s}^{-1}\). What percentage of the incident ultrasound intensity is reflected at this boundary?

Technetium-99m \(^{99\text{m}}\text{Tc}\) is a widely used radioactive tracer in medical imaging.\n(a) In a particular diagnostic procedure, the physical half-life \(T_p\) of \(^{99\text{m}}\text{Tc}\) is \(6.0\text{ hours}\) and its biological half-life \(T_b\) in the target organ is \(24.0\text{ hours}\). Calculate the effective half-life \(T_e\) of the tracer in this organ. (3 marks)\n(b) Explain why \(^{99\text{m}}\text{Tc}\) is highly suitable for medical imaging in terms of its half-life and the type of radiation it emits. (4 marks)\n(c) A patient is injected with the tracer, and the initial activity in the target organ is \(300\text{ MBq}\). Calculate the remaining activity of the tracer in this organ after \(12.0\text{ hours}\). (3 marks)

A distant red giant star has a peak emission wavelength \(\lambda_{\text{max}} = 966\text{ nm}\) and a luminosity \(L = 4000 L_{\odot}\), where \(L_{\odot} = 3.83 \times 10^{26}\text{ W}\) is the luminosity of the Sun. The surface temperature of the Sun is \(T_{\odot} = 5780\text{ K}\).\n(a) Using Wien's displacement law, estimate the surface temperature \(T\) of this red giant star. (Given: Wien's constant \(b = 2.90 \times 10^{-3}\text{ m K}\)). (3 marks)\n(b) By using Stefan-Boltzmann law, calculate the ratio of the radius of this red giant star to that of the Sun, i.e., \(R / R_{\odot}\). (4 marks)\n(c) Briefly describe the final evolutionary stage of this star and the force that supports it against gravitational collapse, assuming its initial main-sequence mass was \(1.5\) solar masses. (3 marks)