2021 HKDSE Physics Practice Paper | DSE Mock

A right-angled glass prism of refractive index \( 1.52 \) has angles \( 30^\circ, 60^\circ, 90^\circ \). The prism is submerged in a liquid of refractive index \( n \). A light ray is incident normally on the face of the prism opposite to the \( 30^\circ \) angle. If the light ray undergoes total internal reflection at the hypotenuse, what is the maximum possible value of \( n \)?

A rigid container holds a fixed mass of an ideal gas at a temperature of \( 27^\circ\text{C} \) and a pressure of \( 1.0 \times 10^5\text{ Pa} \). The gas is heated until the average kinetic energy of its molecules is doubled. What are the new pressure and temperature of the gas?

A ball is projected from the edge of a cliff of height \( 40\text{ m} \) with an initial speed of \( 20\text{ m s}^{-1} \) at an angle of \( 30^\circ \) above the horizontal. What is the angle between the ball's velocity vector and the horizontal just before it hits the ground? (Take \( g = 10\text{ m s}^{-2} \) and ignore air resistance.)

Three identical light bulbs P, Q, and R, each of resistance \( R \), are connected to an ideal battery of constant voltage \( V \). Bulb P is connected in series with the parallel combination of Q and R. A switch S is connected in series with bulb R. When switch S is closed, by what factor does the power dissipated by bulb P change?

A square conducting loop of side length \( 0.1\text{ m} \) and resistance \( 0.2\ \Omega \) is pulled at a constant speed of \( 4\text{ m s}^{-1} \) out of a uniform magnetic field of \( 0.5\text{ T} \) that is perpendicular to the plane of the loop. What is the magnitude of the external force required to maintain this constant speed?

Two blocks A and B of masses \( m_A = 3\text{ kg} \) and \( m_B = 2\text{ kg} \) are connected by a light inextensible string passing over a frictionless pulley. Block A is placed on a rough horizontal table with a coefficient of kinetic friction \( \mu_k = 0.3 \), while block B hangs vertically. The system is released from rest. What is the tension in the string? (Take \( g = 9.81\text{ m s}^{-2} \).)

An electric heater of power \( 200\text{ W} \) is used to heat a metal block of mass \( 0.5\text{ kg} \) and specific heat capacity \( 400\text{ J kg}^{-1}\text{ }^\circ\text{C}^{-1} \). In \( 25\text{ s} \), the temperature of the block rises by \( 20^\circ\text{C} \). What percentage of the thermal energy supplied by the heater is lost to the surroundings?

Two identical loudspeakers, \( S_1 \) and \( S_2 \), are connected to the same signal generator and emit coherent sound waves of frequency \( 850\text{ Hz} \) in phase. A microphone is placed at point \( P \), which is \( 3.2\text{ m} \) from \( S_1 \) and \( 4.4\text{ m} \) from \( S_2 \). The speed of sound in air is \( 340\text{ m s}^{-1} \). What type of sound is heard at \( P \), and how does it change if the frequency is slowly increased from \( 850\text{ Hz} \)?

Two parallel horizontal metal plates are separated by a distance of \( 2.0\text{ cm} \). A potential difference of \( 400\text{ V} \) is applied across them. An oil droplet of mass \( 1.6 \times 10^{-15}\text{ kg} \) remains stationary between the plates. How many excess elementary charges (where \( e = 1.6 \times 10^{-19}\text{ C} \)) does the droplet carry? (Take \( g = 10\text{ m s}^{-2} \).)

In a photoelectric effect experiment, monochromatic light is shone on a metal surface, and the measured stopping potential is \( V_s \). If the frequency of the incident light is doubled, the new stopping potential \( V_s' \) will be:

An insulated container holds \(1.0\text{ kg}\) of water at \(20^\circ\text{C}\). A solid metal block of mass \(0.5\text{ kg}\) at an initial temperature \(T\) is placed into the container. When thermal equilibrium is reached, the final temperature of the mixture is \(15^\circ\text{C}\). Given that the specific heat capacity of water is \(4200\text{ J kg}^{-1}{^\circ}\text{C}^{-1}\) and that of the metal block is \(400\text{ J kg}^{-1}{^\circ}\text{C}^{-1}\), find \(T\). Assume no heat loss to the surroundings and the heat capacity of the container is negligible.

A stone is projected horizontally from the top of a vertical cliff of height \(H\) with an initial speed \(u\). Air resistance is negligible. If the stone strikes the horizontal ground at an angle of \(45^\circ\) to the horizontal, which of the following is a correct expression for \(H\)?

Three identical resistors, each of resistance \(R\), are connected to an ideal battery of constant voltage \(V\). When they are connected in series, the total power dissipated by the circuit is \(P_S\). When they are connected in parallel to the same battery, the total power dissipated is \(P_P\). What is the ratio \(\frac{P_P}{P_S}\)?

A ray of light enters a semi-circular glass block of refractive index 1.50 through its curved surface, directed towards the center \(O\) of the flat boundary. The angle of incidence of the ray at the flat boundary at \(O\) is \(30.0^\circ\). What is the angle of deviation of the ray when it emerges into the air?

A square conducting loop of side length \(L\) and resistance \(R\) is pulled horizontally at a constant speed \(v\) out of a region of uniform magnetic field \(B\). The magnetic field is perpendicular to the plane of the loop. Which of the following is the correct expression for the external force required to maintain this constant speed?

Two blocks of masses \(M\) and \(m\) are connected by a light inextensible string, with the block of mass \(M\) connected to the ceiling by another light inextensible string. The entire system is pulled upwards by the upper string with an upward acceleration \(a\). Let \(T_1\) be the tension in the upper string and \(T_2\) be the tension in the lower string. What is the ratio \(\frac{T_1}{T_2}\)?

A solid substance of mass \(0.20\text{ kg}\) is heated from its initial temperature of \(20^\circ\text{C}\) by a heater of constant power \(100\text{ W}\). The substance reaches its melting point of \(80^\circ\text{C}\) at \(t = 4.0\text{ minutes}\) and is completely melted at \(t = 12.0\text{ minutes}\). What is the specific latent heat of fusion of the substance? (Assume no heat is lost to the surroundings.)

A transverse progressive wave travelling along a horizontal string is represented by the equation:
\[y = 0.05 \sin(4\pi t - 2\pi x)\]
where \(x\) and \(y\) are measured in meters (\(\text{m}\)) and \(t\) is measured in seconds (\(\text{s}\)). What are the wave speed and the direction of travel of this wave?

An object starts from rest and moves along a straight line. It first accelerates uniformly at a constant rate \(a\) for a certain time, and then immediately decelerates uniformly to rest at a constant rate \(2a\). What is the ratio of the average velocity of the object during the entire journey to its maximum velocity?

A potential divider circuit consists of a \(12\text{ V}\) d.c. supply of negligible internal resistance connected in series with a fixed resistor of resistance \(4\ \Omega\) and a light-dependent resistor (LDR). In the dark, the resistance of the LDR is \(8\ \Omega\). Under bright light, the resistance of the LDR decreases to \(2\ \Omega\). What is the change in the potential difference across the LDR when the environment changes from dark to bright light?

Two liquids \(A\) of mass \(100\text{ g}\) and \(B\) of mass \(200\text{ g}\) are heated by identical heaters of constant power \(50\text{ W}\). The temperature of liquid \(A\) rises by \(10\text{ }^\circ\text{C}\) in \(2\text{ minutes}\), while that of liquid \(B\) rises by \(15\text{ }^\circ\text{C}\) in \(3\text{ minutes}\). Assuming no heat loss to the surroundings, find the ratio of the specific heat capacity of \(A\) to that of \(B\) (\(c_A : c_B\)).

A particle is projected from horizontal ground. If the kinetic energy of the particle at its highest point is half of its initial kinetic energy, what is the ratio of its maximum height to its horizontal range?

A block of mass \(2\text{ kg}\) is placed on a rough plane inclined at \(45^\circ\) to the horizontal. The coefficient of static friction between the block and the plane is \(0.25\). A horizontal force \(F\) is applied to the block, pushing it towards the inclined plane. What is the minimum value of \(F\) required to prevent the block from sliding down? (Take \(g = 10\text{ m s}^{-2}\))

A light ray enters a glass prism of refractive index \(n = \sqrt{3}\) and apex angle \(60^\circ\). If the light ray inside the prism travels parallel to the base of the symmetric prism, what is the angle of incidence in air?

A fish is swimming at a depth of \(1.2\text{ m}\) below the water surface. A bird is flying at a height of \(1.8\text{ m}\) directly above the water surface. What is the apparent distance of the bird as seen by the fish? (Take the refractive index of water to be \(\frac{4}{3}\) and that of air to be \(1\))

Three identical resistors, each of resistance \(R\), are connected to form a network. Which of the following cannot be the equivalent resistance of this network?

In a potential divider circuit, a light-dependent resistor (LDR) is connected in series with a \(10\text{ k}\Omega\) fixed resistor across a \(12\text{ V}\) d.c. supply of negligible internal resistance. The output voltage \(V_{\text{out}}\) is measured across the LDR. In the dark, the resistance of the LDR is \(40\text{ k}\Omega\). In bright light, its resistance is \(2\text{ k}\Omega\). What is the change in \(V_{\text{out}}\) when the illumination changes from dark to bright light?

A metal rod of length \(0.4\text{ m}\) rotates at a constant rate of \(300\text{ revolutions per minute}\) (rpm) in a plane perpendicular to a uniform magnetic field of strength \(0.5\text{ T}\). The rotation axis passes through one end of the rod. What is the induced e.m.f. between the two ends of the rod?

Two long straight parallel wires \(X\) and \(Y\) carry currents in opposite directions. The magnetic force per unit length acting on wire \(X\) is \(f\). If the current in \(X\) is doubled, the current in \(Y\) is halved, and the distance between the two wires is tripled, what is the new magnetic force per unit length acting on wire \(X\)?

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

(1) The pressure of the gas is doubled.
(2) The average kinetic energy of the gas molecules is doubled.
(3) The root-mean-square speed of the gas molecules is doubled.

An optical fiber consists of a cylindrical core of refractive index 1.50 surrounded by a cladding of refractive index 1.40. A ray of light is incident from air into the core at an angle \(\theta\) to the normal of the flat end-face of the fiber. Find the maximum value of \(\theta\) for which the light ray will undergo total internal reflection at the core-cladding interface.

A real battery of e.m.f. \(E\) and non-negligible internal resistance \(r\) is connected to a resistor \(R_1\). A second resistor \(R_2\) and a switch \(S\) are connected in series, and this combination is connected in parallel with \(R_1\). An ideal voltmeter is connected across the terminals of the battery, and an ideal ammeter is connected in series with \(R_1\). When the switch \(S\) is closed, how do the readings of the voltmeter and the ammeter change?

Three blocks of masses \(m\), \(2m\), and \(3m\) are connected by light inextensible strings and pulled vertically upwards by a force \(F\). The blocks accelerate upwards. Let \(T_1\) be the tension in the string connecting the block of mass \(m\) and the block of mass \(2m\), and \(T_2\) be the tension in the string connecting the block of mass \(2m\) and the block of mass \(3m\). What is the ratio \(\frac{T_1}{T_2}\)?

A glass prism has a cross-section of a right-angled triangle \(ABC\) with \(\angle A = 90^\circ\), \(\angle B = 60^\circ\), and \(\angle C = 30^\circ\). The refractive index of the glass is \(1.60\). A monochromatic light ray is incident normally on the face \(AB\) from the air.
(a) Calculate the critical angle \(\theta_c\) of the glass-air interface. (2 marks)
(b) Determine whether the light ray will experience total internal reflection when it hits the face \(BC\) for the first time. Show your calculation. (3 marks)
(c) Hence, calculate the angle of deviation of the ray when it finally emerges back into the air from the face \(AC\). (4 marks)

A real battery of electromotive force (e.m.f.) \(E = 12.0\text{ V}\) and internal resistance \(r = 2.0\ \Omega\) is connected to a variable resistor \(R\) as shown in a circuit.
(a) Express the electrical power \(P\) dissipated in the variable resistor \(R\) in terms of \(E\), \(r\), and \(R\). (2 marks)
(b) (i) Show that the power \(P\) can also be written as \(P = \frac{E^2}{(\sqrt{R} - r/\sqrt{R})^2 + 4r}\). (2 marks)
(ii) Hence, find the value of \(R\) that maximizes the power dissipation, and calculate this maximum power \(P_{max}\). (2 marks)
(c) When \(R\) is decreased from \(8.0\ \Omega\) to \(4.0\ \Omega\), explain how the terminal voltage of the battery changes. (3 marks)

A rescue package is dropped from a helicopter flying horizontally at a constant speed of \(u = 40.0\text{ m s}^{-1}\) at an altitude of \(h = 125\text{ m}\) above a flat plain. Ignore air resistance and take the acceleration due to gravity \(g = 9.81\text{ m s}^{-2}\).
(a) Show that the package takes approximately \(5.05\text{ s}\) to hit the ground. (2 marks)
(b) Find the horizontal distance from the point of release where the package lands. (2 marks)
(c) Find the speed of the package just before it hits the ground, and the angle its velocity vector makes with the horizontal. (5 marks)

A flat, circular coil of wire has \(N = 200\) turns and a radius of \(r = 5.0\text{ cm}\). The coil is placed in a uniform magnetic field that is perpendicular to the plane of the coil. The magnetic field strength \(B\) varies with time \(t\) as shown by the relation \(B(t) = 0.50 - 1.20t\) (for \(t \le 0.40\text{ s}\)), where \(B\) is in teslas (\(\text{T}\)) and \(t\) is in seconds (\(\text{s}\)).
(a) State Faraday's law of electromagnetic induction. (2 marks)
(b) Calculate the rate of change of magnetic flux linkage through the coil. (3 marks)
(c) Calculate the magnitude of the induced electromotive force (e.m.f.) in the coil. (2 marks)
(d) If the coil has a total resistance of \(4.0\ \Omega\), find the induced current, and state its direction (clockwise or counter-clockwise) when viewed from above if the magnetic field initially points vertically upwards. (2 marks)

Block \(A\) of mass \(m_A = 4.0\text{ kg}\) lies on a rough horizontal table. It is connected by a light inextensible string passing over a frictionless pulley to block \(B\) of mass \(m_B = 6.0\text{ kg}\) which hangs vertically. The coefficient of kinetic friction between block \(A\) and the table is \(\mu_k = 0.25\). Take \(g = 9.81\text{ m s}^{-2}\).
(a) Draw the labeled free-body diagrams for both blocks \(A\) and \(B\). (2 marks)
(b) Write down the equations of motion for both blocks when they are released from rest. (2 marks)
(c) Calculate the acceleration of the blocks. (3 marks)
(d) Find the tension in the string. (2 marks)

An electric kettle rated at \(2200\text{ W}\) is used to heat \(0.80\text{ kg}\) of water initially at \(20.0^\circ\text{C}\) to boiling. After the water starts boiling, the kettle is left on for another \(2.0\text{ minutes}\) before it is switched off.
Given: Specific heat capacity of water \(c_w = 4200\text{ J kg}^{-1}\ ^\circ\text{C}^{-1}\), latent heat of vaporization of water \(l_v = 2.26 \times 10^6\text{ J kg}^{-1}\). Assume \(85\%\) of the electrical energy is transferred to the water.
(a) Calculate the time taken for the water to reach \(100.0^\circ\text{C}\) from \(20.0^\circ\text{C}\). (3 marks)
(b) Calculate the mass of water that has evaporated during the \(2.0\text{ minutes}\) of boiling. (4 marks)
(c) Suggest one reason why the efficiency of the kettle is less than \(100\%\). (2 marks)

An ideal gas is sealed in a container of volume \(V_1 = 3.0 \times 10^{-3}\text{ m}^3\) at a temperature of \(27.0^\circ\text{C}\) and a pressure of \(1.5 \times 10^5\text{ Pa}\).
(a) Calculate the number of gas molecules in the container. Take the Boltzmann constant \(k = 1.38 \times 10^{-23}\text{ J K}^{-1}\). (3 marks)
(b) The gas is now compressed isothermally to a volume of \(1.2 \times 10^{-3}\text{ m}^3\). Find the new pressure of the gas. (2 marks)
(c) The gas is then heated at constant volume until its pressure becomes \(4.5 \times 10^5\text{ Pa}\). Calculate the final temperature of the gas in \(^\circ\text{C}\). (4 marks)

A satellite of mass \(m = 800\text{ kg}\) orbits the Earth in a stable circular path with an orbital period of \(2.0\text{ hours}\).
Given: Earth's mass \(M = 5.97 \times 10^{24}\text{ kg}\), Gravitational constant \(G = 6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2}\).
(a) Calculate the angular velocity \(\omega\) of the satellite. (2 marks)
(b) Derive an expression relating the orbital radius \(r\) to the period \(T\), and calculate the orbital radius of this satellite. (4 marks)
(c) Find the magnitude of the gravitational force acting on the satellite. (3 marks)

The nuclear fusion of deuterium (\({}^2_1\text{H}\)) and tritium (\({}^3_1\text{H}\)) is a promising source of clean energy:
\({}^2_1\text{H} + {}^3_1\text{H} \rightarrow {}^4_2\text{He} + {}^1_0\text{n} + \Delta E\)
Given the following rest masses:
\(m({}^2_1\text{H}) = 2.014102\text{ u}\)
\(m({}^3_1\text{H}) = 3.016049\text{ u}\)
\(m({}^4_2\text{He}) = 4.002603\text{ u}\)
\(m({}^1_0\text{n}) = 1.008665\text{ u}\)
\(1\text{ u} = 931.5\text{ MeV}\)
(a) Define "mass defect" in the context of nuclear reactions. (2 marks)
(b) Calculate the mass defect \(\Delta m\) of this fusion reaction in atomic mass units (\(\text{u}\)). (3 marks)
(c) Calculate the energy \(\Delta E\) released in a single fusion event in \(\text{MeV}\). (2 marks)
(d) Explain, in terms of binding energy, why this fusion reaction releases energy. (2 marks)

Two exoplanets orbit a distant star in circular orbits of radii \(r_1\) and \(r_2 = 4r_1\). If the orbital speed of the first planet is \(v_1\), what is the orbital speed of the second planet \(v_2\)?

A galaxy is observed to have a redshift in its spectral line of hydrogen. The wavelength of a line normally at \(656.3\text{ nm}\) is measured as \(672.7\text{ nm}\). If the Hubble constant is \(H_0 = 70\text{ km s}^{-1}\text{ Mpc}^{-1}\), find the distance to this galaxy.

A star has a mass about 10 times the mass of the Sun. When it leaves the main sequence, what is its most likely evolutionary path and final remnant?

Monochromatic light of wavelength \(\lambda\) shines on a metal surface, ejecting photoelectrons with maximum kinetic energy \(K_1\). When light of wavelength \(\lambda / 2\) shines on the same metal surface, the maximum kinetic energy of the photoelectrons is \(K_2\). What is the relation between \(K_2\) and \(K_1\)?

According to Bohr's model of the hydrogen atom, the orbital radius of the electron in the \(n\)-th state is proportional to \(n^2\). If the de Broglie wavelength of the electron in the ground state (\(n=1\)) is \(\lambda_1\), what is the de Broglie wavelength of the electron in the state \(n=3\)?

Why does a Transmission Electron Microscope (TEM) have a much higher resolution than a standard optical microscope?

The solar power intensity reaching the ground is \(800\text{ W m}^{-2}\). A household solar panel system with an efficiency of \(15\%\) is installed on a roof. To generate a constant electrical power of \(3.6\text{ kW}\) under this sunlight, what is the minimum area of solar panels required?

A wind turbine has blades of length \(L\). When the wind speed is \(v\), the maximum theoretical power that can be extracted from the wind is \(P\). If the wind speed increases to \(2v\) and the blade length is increased to \(1.5L\), what is the new maximum theoretical power extracted from the wind?

An ultrasound wave travels from muscle (acoustic impedance \(Z_1 = 1.70 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\)) to bone (acoustic impedance \(Z_2 = 7.80 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\)). What percentage of the ultrasound intensity is reflected at the boundary?

A person with presbyopia has a near point of \(80\text{ cm}\). What refractive power (in dioptres, D) of the contact lenses is needed to allow them to read a book comfortably at a distance of \(25\text{ cm}\)?

Star A has a surface temperature of \(3000\text{ K}\) and a luminosity of \(100 L_\odot\), where \(L_\odot\) is the solar luminosity. Star B has a surface temperature of \(6000\text{ K}\) and a luminosity of \(16 L_\odot\). If both stars can be modeled as blackbodies, find the ratio of the radius of star A to that of star B, \(R_A / R_B\).

A planet orbits a distant star in an elliptical path. The ratio of its maximum distance (aphelion) to its minimum distance (perihelion) from the star is \(3:1\). If the speed of the planet at perihelion is \(v\), what is its speed at aphelion?

In a photoelectric effect experiment, when light of frequency \(f\) is incident on a metal surface, the stopping potential is \(V_0\). When light of frequency \(1.5f\) is incident on the same metal surface, the stopping potential becomes \(2V_0\). What is the work function of the metal?

In the Bohr model of the hydrogen atom, the orbital radius \(r_n\) of the electron in the \(n\)-th energy level is proportional to \(n^2\), and the orbital speed \(v_n\) is proportional to \(1/n\). Find the ratio of the orbital period of the electron in the \(n = 3\) energy level to that in the \(n = 1\) energy level.

A solar water heater is used to heat \(50\text{ kg}\) of water from \(20^\circ\text{C}\) to \(60^\circ\text{C}\) in \(2\text{ hours}\). The average solar radiation power incident on the collector panel of area \(2.5\text{ m}^2\) is \(700\text{ W m}^{-2}\). What is the energy efficiency of the solar water heater? (Given: specific heat capacity of water = \(4200\text{ J kg}^{-1}\text{ }^\circ\text{C}^{-1}\))

A patient can only see objects clearly if they are located between \(50\text{ cm}\) and \(300\text{ cm}\) from their eyes. In order to correct their distance vision so that they can see objects at infinity clearly, what is the power of the spectacle lens required, and what will be the new near point of the eye when wearing these spectacles? (Assume the distance between the spectacles and the eyes is negligible.)

In an experiment on the photoelectric effect, monochromatic light is shone on a photocell with a sodium-coated cathode. The work function of sodium is \(2.28\text{ eV}\).\n\n(a)\n(i) Calculate the threshold frequency of sodium. (2 marks)\n(ii) Calculate the maximum kinetic energy (in \(\text{eV}\)) of the emitted photoelectrons when light of frequency \(7.0 \times 10^{14}\text{ Hz}\) is used. (2 marks)\n\n(b) The intensity of the light is doubled while the frequency is kept at \(7.0 \times 10^{14}\text{ Hz}\). State and explain the change, if any, on:\n(i) the stopping potential. (2 marks)\n(ii) the saturation photocurrent. (2 marks)\n\n(c) The photocell is connected to a microammeter and a variable voltage supply to study the current-voltage (\(I-V\)) characteristic. Sketch a graph of current \(I\) against applied voltage \(V\) for the two light intensities. Label the curves clearly as \(I_1\) (original intensity) and \(I_2\) (doubled intensity). (2 marks)

A wind turbine has blades of length \(L = 25\text{ m}\). It is installed in an area with an average wind speed of \(v = 8.0\text{ m s}^{-1}\). The density of air is \(\rho = 1.2\text{ kg m}^{-3}\).\n\n(a) Show that the maximum kinetic energy of wind passing through the area swept by the blades per second (wind power \(P_w\)) is given by \(P_w = \frac{1}{2} \pi \rho L^2 v^3\). Hence, calculate the value of \(P_w\). (3 marks)\n\n(b) The turbine converts \(35\%\) of this wind power into electrical power. Calculate the electrical power output \(P_e\) of the wind turbine. (2 marks)\n\n(c) The generator produces electricity at a voltage of \(690\text{ V}\), which is stepped up to \(33\text{ kV}\) for transmission.\n(i) Suggest ONE reason why the voltage is stepped up. (1 mark)\n(ii) If the electrical power \(P_e\) is transmitted through cables of total resistance \(4.0\ \Omega\), calculate the power loss in the cables. (2 marks)\n\n(d) State ONE environmental advantage and ONE limitation of wind power compared to coal-fired power stations. (2 marks)