2024 HKDSE Physics Practice Paper | DSE Mock

An electric heater of power \(50\text{ W}\) is used to heat a solid block of mass \(0.2\text{ kg}\) initially at its melting point. During the heating process, heat is lost to the surroundings at a constant rate of \(10\text{ W}\). If the specific latent heat of fusion of the substance is \(2.0 \times 10^5\text{ J kg}^{-1}\), find the time \(t\) required to melt the block completely.

A fixed mass of an ideal gas is contained in a cylinder with a movable piston. The volume of the gas is slowly halved isothermally. Then, the gas is heated at constant pressure until its volume returns to the original volume. Which of the following statements about the final state of the gas (compared to its initial state) is correct?

A block of mass \(4\text{ kg}\) is pushed up a rough inclined plane of inclination angle \(30^\circ\) by a constant horizontal force \(F = 50\text{ N}\). If the block moves up the incline at a constant speed, what is the magnitude of the frictional force acting on the block? (Take \(g = 9.8\text{ m s}^{-2}\))

A toy car of mass \(0.5\text{ kg}\) starts from rest and moves along a horizontal track. The power \(P\) delivered to the car as a function of time \(t\) is given by \(P = 3t\text{ W}\) (for \(t \ge 0\)). Assuming that there is no energy loss, find the speed of the car at \(t = 4\text{ s}\).

A small coin is placed on a horizontal turntable at a distance of \(0.2\text{ m}\) from the center. The turntable starts from rest and accelerates slowly. If the coefficient of static friction between the coin and the turntable is \(0.5\), find the maximum angular speed of the turntable before the coin starts to slip. (Take \(g = 9.8\text{ m s}^{-2}\))

A light ray is incident at the boundary between medium X and medium Y. The refractive index of medium X is \(1.6\) and that of medium Y is \(1.2\). What is the critical angle for total internal reflection, and in which medium must the light be incident for total internal reflection to occur?

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 in the circuit is \(P_s\). When they are connected in parallel, the total power dissipated is \(P_p\). What is the ratio \(P_p / P_s\)?

A flat circular coil of \(200\) turns and area \(0.05\text{ m}^2\) is placed perpendicular to a uniform magnetic field of strength \(0.4\text{ T}\). The magnetic field is reduced to zero at a constant rate within a time interval of \(0.2\text{ s}\). What is the magnitude of the average induced electromotive force (e.m.f.) in the coil?

A sample contains a mixture of two radioactive isotopes, A and B. Initially, the activity of A is \(1600\text{ Bq}\) and the activity of B is \(100\text{ Bq}\). The half-life of A is \(3\text{ hours}\), and the half-life of B is \(6\text{ hours}\). After how many hours will the activities of the two isotopes in the sample become equal?

A ball of mass \(0.2\text{ kg}\) is dropped from a height of \(2.50\text{ m}\) onto a hard horizontal floor. It rebounds to a maximum height of \(0.90\text{ m}\). If the collision between the ball and the floor lasts for \(0.05\text{ s}\), what is the magnitude of the average force exerted by the floor on the ball? (Take \(g = 9.8\text{ m s}^{-2}\))

An insulated container of negligible heat capacity contains 0.2 kg of water at 20°C. A 0.05 kg block of ice at 0°C is added to the container. Assume no heat loss to the surroundings. Which of the following statements about the mixture when it reaches thermal equilibrium is/are correct? (Given: specific heat capacity of water = 4200 J kg^{-1} °C^{-1}; specific latent heat of fusion of ice = 3.34 \times 10^5 J kg^{-1}) (1) All ice has melted. (2) The final temperature of the mixture is 0°C. (3) If the initial temperature of the water were 15°C, some ice would remain unmelted.

An ideal gas is enclosed in a rigid container of fixed volume. When the absolute temperature of the gas is doubled, which of the following statements is/are correct? (1) The root-mean-square speed of the gas molecules is doubled. (2) The collision frequency between gas molecules and the container walls is doubled. (3) The pressure of the gas is doubled.

Two blocks of masses m_1 = 3 kg and m_2 = 1 kg are connected by a light inextensible string passing over a smooth light pulley. Block m_1 is placed on a rough horizontal table with coefficient of kinetic friction \mu = 0.2. Block m_2 hangs vertically. When the system is released from rest, what is the magnitude of the acceleration of the blocks? (Take the acceleration due to gravity as g.)

Trolley A of mass 2 kg moving at 3 m s^{-1} to the right collides head-on with trolley B of mass 1 kg moving at 1 m s^{-1} to the left. After the collision, trolley A continues to move to the right at 1 m s^{-1}. Which of the following describes the change in momentum of trolley B and the nature of the collision?

A satellite orbits the Earth in a circular orbit of radius r with a speed v and an orbital period T. If the satellite is moved to a new circular orbit of radius 4r, what will be its new speed and orbital period?

An object is placed at a distance u from a thin converging lens of focal length 10 cm. A real, inverted image is formed. If the magnification of the image is 2, find the value of u.

Two resistors R_1 and R_2, each of resistance 6 \Omega, are connected in parallel. This combination is connected in series with a third resistor R_3, also of resistance 6 \Omega. The entire circuit is connected across an ideal battery of electromotive force (emf) 18 V. What are the potential difference across R_1 and the total power dissipated in the circuit?

A bar magnet is dropped vertically, north pole pointing downwards, through a horizontal copper ring. Which of the following statements is/are correct? (1) As the north pole approaches the ring from above, the induced current in the ring (viewed from above) is anticlockwise. (2) As the south pole of the magnet leaves the ring from below, the induced current in the ring (viewed from above) is anticlockwise. (3) The acceleration of the falling magnet is less than the acceleration due to gravity g both when it is approaching and when it is leaving the ring.

An alternating voltage v = 220\sqrt{2} \sin(100\pi t) V is connected across a resistor of resistance 44 \Omega. What are the root-mean-square (rms) current in the resistor and the average power dissipated?

A radioactive sample contains a mixture of two radioisotopes, X and Y. Initially, the activity of X is 1600 Bq and the activity of Y is 200 Bq. The half-life of X is 3 hours, and the half-life of Y is 6 hours. After how many hours will the activities of X and Y be equal?

A \(0.5\text{ kg}\) block of ice at \(-10 ^\circ\text{C}\) is heated by a \(100\text{ W}\) heater. Find the time taken to melt all the ice into water at \(0 ^\circ\text{C}\). (Given: specific heat capacity of ice \(= 2100\text{ J kg}^{-1}{^\circ}\text{C}^{-1}\), specific latent heat of fusion of ice \(= 3.34 \times 10^5\text{ J kg}^{-1}\))

A rigid gas cylinder contains an ideal gas at a pressure of \(P\) and a temperature of \(27 ^\circ\text{C}\). After some gas leaks out, the pressure becomes \(0.6 P\) and the temperature decreases to \(7 ^\circ\text{C}\). Find the fraction of the original mass of gas that remains in the cylinder.

A car starts from rest and accelerates uniformly to a speed of \(10\text{ m s}^{-1}\) in \(4\text{ s}\). It then travels at this constant speed for \(4\text{ s}\), and finally decelerates uniformly to rest in \(2\text{ s}\). What is the average speed of the car for the entire \(10\text{ s}\) journey?

A block of mass \(2\text{ kg}\) is placed on a rough inclined plane making an angle of \(30^\circ\) with the horizontal. The coefficient of static friction between the block and the plane is \(0.6\). What is the magnitude of the friction force acting on the block? (Take \(g = 9.8\text{ m s}^{-2}\))

A light spring of force constant \(100\text{ N m}^{-1}\) hangs vertically with a \(0.5\text{ kg}\) block attached to its lower end. The block is initially at rest at its equilibrium position. It is then pulled vertically downwards by \(0.1\text{ m}\) and released from rest. What is the maximum kinetic energy of the block during the subsequent motion?

Two satellites, \(P\) and \(Q\), orbit the Earth in circular orbits. The mass of \(P\) is half that of \(Q\), and the kinetic energy of \(P\) is twice that of \(Q\). What is the ratio of the orbital radius of \(P\) to that of \(Q\)?

A ray of light travels from medium \(X\) to medium \(Y\). The angle of incidence in \(X\) is \(30^\circ\) and the angle of refraction in \(Y\) is \(45^\circ\). What is the critical angle for total internal reflection when light travels from one medium to the other?

A string of fixed length is clamped at both ends. When it vibrates in its third harmonic, the frequency is \(120\text{ Hz}\). What is the frequency of the vibration when it is excited to its fifth harmonic?

Three identical resistors are connected to a DC source of constant voltage \(V\). When they are connected in series, the total power dissipated is \(P_1\). When they are connected in parallel to the same source, the total power dissipated is \(P_2\). What is the ratio \(\frac{P_1}{P_2}\)?

A flat coil of \(50\) turns has an area of \(0.2\text{ m}^2\). It is placed in a uniform magnetic field perpendicular to the plane of the coil. If the magnetic field strength decreases from \(0.8\text{ T}\) to \(0.2\text{ T}\) at a constant rate in \(0.3\text{ s}\), what is the magnitude of the average induced electromotive force (emf) in the coil?

A small block of mass \(m\) is placed on a rough horizontal turntable rotating at a constant angular speed \(\omega\). The distance from the block to the center of rotation is \(r\). The coefficient of static friction between the block and the turntable is \(\mu\). If the angular speed is doubled and the distance from the center is halved, what is the new minimum coefficient of static friction required to prevent the block from slipping?

A copper ring is dropped vertically through the center of a strong bar magnet fixed vertically on a table (with its North pole facing upwards). Which of the following statements about the magnetic force acting on the ring is/are correct as it falls? (1) Before the ring passes the magnet, the magnetic force on it is upwards. (2) When the ring is exactly at the midpoint of the magnet, the magnetic force on it is zero. (3) After the ring passes the magnet, the magnetic force on it is downwards.

A ray of monochromatic light travels from medium X to medium Y. The angle of incidence in medium X is \(30^\circ\), and the angle of refraction in medium Y is \(45^\circ\). What is the ratio of the speed of light in medium X to that in medium Y?