▶️ Answer/Explanation
Detailed solution:
A metre ruler is typically graduated in millimetres (mm), which is its smallest division.
One millimetre is equal to 0.001 metres (10⁻³ m).
Therefore, a measurement taken to the nearest millimetre must be recorded to three decimal places when expressed in metres.
Option B (0.293 m) shows three decimal places, representing 293 mm.
Options C and D are less precise, while option A suggests a level of precision (0.1 mm) that a standard ruler cannot provide.
▶️ Answer/Explanation
Detailed solution:
Distance travelled is found using the equation: distance = average speed × time taken.
Convert time to seconds: 2 min = 120 s.
Distance = 6 km/s × 120 s = 720 km.
This matches option C directly.
Options A and B arise from omitting the seconds conversion; D results from treating time as hours instead of minutes.
Thus, the correct answer is C.
▶️ Answer/Explanation
Detailed solution:
As the ball falls, air resistance (drag) increases with speed, so the net downward force (weight – drag) decreases.
Since resultant force decreases but is still downward, acceleration (a = F/m) also decreases but remains downward.
The ball speeds up, but at a decreasing rate, until terminal velocity would be reached.
Thus, both resultant force and acceleration decrease.
▶️ Answer/Explanation
Detailed solution:
Ignoring air resistance, the coconut is in free fall under gravity. Its acceleration is the constant acceleration of free fall \(g \approx 9.8 \, m/s^2\) at all points during the fall, including at X and Y. Thus, the acceleration is the same at both points.
▶️ Answer/Explanation
Detailed solution:
When a car moves at constant speed around a bend, its velocity direction changes, so it accelerates toward the centre.
This centripetal acceleration requires a resultant force perpendicular to motion, directed inward.
▶️ Answer/Explanation
Detailed solution:
For equilibrium, the net force and net moment must be zero. The hinge force must balance the weight (down) and cable tension (up-left). Summing horizontal forces requires hinge force to have a rightward component; summing vertical forces requires it to have an upward component, matching arrow D.
▶️ Answer/Explanation
Detailed solution:
Impulse equals change in momentum, and impulse is defined as force multiplied by the time interval over which it acts.
Force/area gives pressure, not momentum change. Force × distance gives work done, not momentum change. Force × (distance/time) is force × speed, which is power.
Therefore, the correct relationship is momentum change = force × time.
▶️ Answer/Explanation
Detailed solution:
Nuclear fuel releases energy through nuclear fission, where heavy nuclei split into smaller nuclei. It does not originate from the Sun (unlike solar or wind). Nuclear waste has significant environmental impact. Power stations use turbines to generate electricity from heat produced by fission. Thus, option D is correct.
▶️ Answer/Explanation
Detailed solution:
Initial kinetic energy = \(\frac{1}{2}mv^2\).
At Q, gain in GPE = mgh and work done against air resistance = W.
By energy conservation, final KE = initial KE – gain in GPE – work done against resistance = \(\frac{1}{2}mv^2 – mgh – W\).
▶️ Answer/Explanation
Detailed solution:
Total input energy = 560 J.
Useful energy output (light + sound + kinetic) = 120 J + 120 J + 120 J = 360 J.
Wasted energy = total input − useful output = 560 J − 360 J = 200 J.
▶️ Answer/Explanation
Detailed solution:
Pressure is defined as force per unit area, \(p = \frac{F}{A}\). The total weight is 45000 N, supported by four feet.
The force on one foot is \(F = \frac{45000}{4} = 11250\text{ N}\). Using \(A = \frac{F}{p}\), the area is \(A = \frac{11250}{34000} \approx 0.33\text{ m}^2\).
This calculation applies the direct relationship between pressure, force, and area for a single foot.
Thus, the area of each foot is approximately 0.33 m², matching option B.
▶️ Answer/Explanation
Detailed solution:
Heating the container increases the average kinetic energy of the trapped air particles, causing them to move faster.
Faster-moving particles collide with the container walls more frequently and with greater force, increasing the pressure inside.
The number of particles and the volume of the container remain constant; individual particles do not expand.
This aligns with the kinetic particle model where gas pressure is due to particle collisions with surfaces.
Therefore, the increased pressure is caused by the air particles moving more quickly.
▶️ Answer/Explanation
Detailed solution:
Internal energy is the total kinetic and potential energy of particles in a substance, and it depends on mass, temperature, and state.
When the temperature of the coffee falls, the average kinetic energy of its particles decreases, leading to a decrease in internal energy.
Option A is incorrect due to energy conservation; the coffee’s energy loss equals the pool water’s energy gain.
Option B is false because internal energy also depends on mass and phase, not just temperature.
Option C is incorrect since the pool has vastly more mass, giving it much greater total internal energy despite its lower temperature.
Thus, only option D correctly describes the relationship between temperature change and internal energy.
▶️ Answer/Explanation
Detailed solution:
The mass decreases because water molecules at the surface gain enough kinetic energy from the warm surroundings to escape into the air as vapor.
This process is evaporation, which occurs at any temperature below boiling point when the liquid is exposed to open air.
Freezing would turn water to solid ice without a change in mass, while condensation would increase mass as vapor becomes liquid.
Boiling requires the entire liquid to reach 100°C, which is not indicated in a warm room setting over two hours.
Therefore, the continuous loss of mass is best explained by the evaporation of water into the surrounding air.
Hence, option A is correct.
▶️ Answer/Explanation
Detailed solution:
The specific heat capacity of a material is the energy needed to raise the temperature of 1 kg of the substance by 1°C.
Since the same mass of aluminium requires more energy for the same temperature rise, it has a higher specific heat capacity.
Thermal conductivity (options A and B) relates to the rate of energy transfer, not the amount of energy stored per degree.
Option D is incorrect because a lower specific heat capacity would mean less energy is required for the temperature change.
Therefore, aluminium stores more internal energy per degree of temperature rise compared to copper.
Hence, option C is the correct scientific explanation.
▶️ Answer/Explanation
Detailed solution:
The horizontal sections of the graph represent changes of state where temperature remains constant.
The first plateau corresponds to melting (ice to water), completing at point Q.
The second plateau corresponds to boiling (water to steam), completing at point S.
During these phase changes, supplied energy increases internal potential energy without raising temperature.
Therefore, the ice completely changes to water at Q and water completely changes to steam at S.
▶️ Answer/Explanation
Detailed solution:
When a wave is reflected at a plane surface, its direction of propagation changes according to the law of reflection.
The frequency of a wave is determined by the source and remains constant during reflection.
Since the wave remains in the same medium, its speed and therefore its wavelength also remain unchanged.
Reflection only alters the path of the wave, causing it to bounce back or change direction.
Thus, only the direction of propagation is modified by the reflection process.
▶️ Answer/Explanation
Detailed solution:
Light slows down when entering an optically denser medium. Glass and water are both denser than air, so speed decreases at air-glass (W) and air-water (Y) boundaries. At point X, light moves from glass to water (both denser media), and at point Z it exits water to air, where speed increases. Since the question asks where speed decreases, the correct points are W (air to glass) and Y (air to water). Thus, option B correctly identifies the two interfaces where light enters a denser medium and slows down.
▶️ Answer/Explanation
Detailed solution:
Diffraction is the spreading of waves after passing through a narrow gap or around an obstacle.
When plane waves encounter a gap comparable to their wavelength, they emerge as circular wavefronts centered on the gap.
The diagram in option C correctly shows this curved, spreading pattern rather than waves continuing in straight lines.
The wavefronts remain continuous and the wavelength stays the same during diffraction.
Options showing straight wavefronts after the gap do not represent the correct diffraction pattern.
▶️ Answer/Explanation
Detailed solution:
The angle of incidence i is measured between the incident ray and the normal at the point of incidence on the boundary.
The angle of refraction r is measured between the refracted ray and the normal inside the plastic wedge.
The critical angle c is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°.
In diagram B, i and r are correctly shown at the air-plastic boundary, and c is correctly labelled at the plastic-air boundary where total internal reflection occurs.
All angles are drawn with respect to the appropriate normals, matching the standard definitions used in optics.
Therefore, option B represents the correct labelling of angles i, r, and c.
▶️ Answer/Explanation
Detailed solution:
From the scale diagram, the object distance u = 20 cm, and the image distance v is measured as 20 cm on the opposite side.
Using the lens formula 1/f = 1/u + 1/v gives 1/f = 1/20 + 1/20 = 1/10, so the focal length f = 10 cm.
The image is real, inverted, and formed at a distance of 20 cm from the lens, which matches the values in row A.
Therefore, the focal length is 10 cm and the image distance is 20 cm, confirming option A as correct.
▶️ Answer/Explanation
Detailed solution:
The wave equation relates speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) as \(v = f\lambda\).
For all electromagnetic waves, including radio waves, the speed in a vacuum is \(v = 3.0 \times 10^{8} \text{ m/s}\).
Rearranging the formula to solve for wavelength gives \(\lambda = \frac{v}{f} = \frac{3.0 \times 10^{8}}{2.0 \times 10^{5}}\).
Performing the calculation yields \(\lambda = 1.5 \times 10^{3} \text{ m}\), which is equivalent to 1500 m.
This result correctly corresponds to option D, which is the appropriate wavelength for this radio frequency.
▶️ Answer/Explanation
Detailed solution:
Sound waves are longitudinal waves, meaning the particles vibrate parallel to the direction of energy transfer.
Since the loudspeaker pushes the air horizontally towards the flame, the air particles oscillate left and right.
The flame, being light and responsive to air movement, vibrates in the same left and right direction as the particles.
This left-right oscillation confirms the wave is longitudinal, as the disturbance is parallel to propagation.
Therefore, option C correctly identifies both the horizontal vibration and the longitudinal nature of the wave.
▶️ Answer/Explanation
Detailed solution:
The strength of a magnetic field is indicated by the spacing of the magnetic field lines.
Where the field lines are closest together, the magnetic field is strongest and the force on a magnetic pole is greatest.
In the diagram, the field lines are most concentrated at position A, near the poles of the magnet.
As the field lines spread out at positions B, C, and D, the field strength decreases.
Therefore, a magnetic pole placed at position A will experience the strongest force.
▶️ Answer/Explanation
Detailed solution:
Electric current is defined as the rate of flow of charge, given by the equation I = Q / t.
First, convert the time from minutes to seconds: 2.5 min = 2.5 × 60 = 150 s.
Rearrange the equation to solve for charge: Q = I × t = 0.60 A × 150 s.
Multiplying gives Q = 90 C, meaning 90 coulombs of charge pass the point.
Options A and B result from incorrect unit conversions or misapplication of the formula.
Therefore, option C is the correct choice for the charge passing the point.
▶️ Answer/Explanation
Detailed solution:
The unit J/C represents energy transferred per unit charge, which is the definition of the volt (V).
Both electromotive force (e.m.f.) and potential difference (p.d.) are measured in volts and are defined as work done or energy transferred per unit charge.
Charge is measured in coulombs (C) and energy in joules (J), so neither has the unit J/C alone.
Since 1 V = 1 J/C, both e.m.f. and p.d. share this unit, making option C the correct answer.
▶️ Answer/Explanation
Detailed solution:
Resistance R is proportional to length L and inversely proportional to cross-sectional area A (R ∝ L/A).
Since area A is proportional to diameter², quartering the diameter reduces A by a factor of 16.
Doubling the length increases resistance by a factor of 2, while the area reduction increases it by a factor of 16.
The combined effect is 2 × 16 = 32, so the new resistance is 32 times the original.
Therefore, the ratio of the original resistance to the new resistance is 1 : 32.
This matches option D.
▶️ Answer/Explanation
Detailed solution:
A diode is a component that allows current to flow in only one direction, indicated by the triangle and line symbol.
In option C, the diode is placed in series with a fixed resistor, meaning they share the same current path.
Options A, B, and D either show the diode in parallel, no diode, or an incorrect arrangement.
The resistor limits current, protecting the diode from excessive flow in the forward direction.
Therefore, circuit C correctly shows a diode connected in series with a fixed resistor.
▶️ Answer/Explanation
Detailed solution:
Resistors X and Y are connected in parallel, so the current from the cell splits between the two branches.
Since X has twice the resistance of Y, the current through X is half the current through Y.
The total current from the cell is the sum of the currents in X and Y, making it greater than the current in X alone.
In a parallel circuit, the potential difference across each branch is equal to the cell’s p.d., so C and D are incorrect.
Therefore, option A correctly states that the current in the cell is greater than the current in X.
▶️ Answer/Explanation
Detailed solution:
In a series circuit, the current is the same everywhere. For the 8 Ω resistor, I = V/R = 36/8 = 4.5 A.
This same current flows through the 4 Ω resistor, so V = IR = 4.5 × 4 = 18 V.
Alternatively, the potential divider principle gives V₁/V₂ = R₁/R₂, so V₄/36 = 4/8, yielding V₄ = 18 V.
The total supply voltage would be 36 V + 18 V = 54 V, which is consistent with the series arrangement.
Therefore, the voltmeter reading across the 4 Ω resistor is 18 V, making option B correct.
▶️ Answer/Explanation
Detailed solution:
To induce a current from Y to X, apply Fleming’s right-hand rule with the magnetic field directed downward (N to S).
Pointing the thumb out of the paper, towards the observer, aligns the second finger to indicate current flow from Y to X.
Motion parallel to the field or in the opposite direction would not produce the correct current orientation.
Therefore, the rod must be moved out of the paper, towards the observer.
▶️ Answer/Explanation
Detailed solution:
In a basic d.c. motor, the coil rotates between the poles of a permanent magnet.
The ends of the coil are connected to a split-ring commutator, which reverses the current direction every half turn to maintain continuous rotation.
Carbon brushes press against the commutator to provide electrical connections from the external circuit to the rotating coil.
The diagram labels feature 1 as the permanent magnet, feature 2 as the split-ring commutator, and feature 3 as the brushes.
Option B correctly identifies these three essential components of the d.c. motor.
Therefore, option B is the correct choice.
▶️ Answer/Explanation
Detailed solution:
For each 100% efficient transformer, power in equals power out: IₚVₚ = IₛVₛ. With turns ratio Nₚ/Nₛ = 2, voltage halves and current doubles at each step-down stage.
Working backwards from Q’s secondary (0.2 A), Q’s primary current is 0.1 A, which is P’s secondary current.
P’s primary current is therefore half of its secondary current, giving 0.05 A.
Thus, the current supplied to the primary of transformer P is 0.05 A.
▶️ Answer/Explanation
Detailed solution:
Most α-particles pass through with little deflection, indicating the atom is mostly empty space.
The large-angle scattering of a few α-particles shows they encountered a dense, positively charged centre.
This centre, the nucleus, must contain most of the atom’s mass to cause such significant deflection.
Options A and D incorrectly describe the mass or charge distribution, while B reflects the outdated plum pudding model.
Thus, the evidence supports a tiny, massive, charged nucleus, making option C correct.
▶️ Answer/Explanation
Detailed solution:
Alpha particles have a large mass and double positive charge, making them strongly ionising as they collide with atoms.
Because they lose energy rapidly through this ionisation, they have very low penetration and can be stopped by paper or skin.
Beta particles are much lighter, faster, and singly charged, so they are less ionising and therefore penetrate further into materials like aluminium.
Thus, the statement “Alpha-particles are less penetrating than beta-particles because alpha-particles are more ionising” is correct.
Therefore, option B accurately describes the inverse relationship between ionising ability and penetrating power for these two types of radiation.
▶️ Answer/Explanation
Detailed solution:
In alpha decay, the unstable nucleus emits an alpha particle (2 protons and 2 neutrons).
This changes the proton number, transforming the original element into a new, different element.
Decay is a random process, not tied to a specific time like one half-life, and does not stop after two half-lives.
The process involves nuclear changes, not the loss of orbital electrons from the atom.
Therefore, the statement that the nucleus changes to a different element is correct.
Option B is the accurate description of alpha decay.
▶️ Answer/Explanation
Detailed solution:
After 1 half-life, 50% remains; after 2 half-lives, 25% remains; after 3 half-lives, 12.5% remains.
Since 12.5% is left after 90.0 years, this time period must correspond to exactly 3 half-lives.
Therefore, one half-life is calculated as \( \frac{90.0 \text{ years}}{3} = 30.0 \text{ years} \).
This matches the definition of half-life as the time for the activity (or quantity) to halve.
Option C is correct as 30.0 years is the required time for the isotope to decay to half its previous amount.
▶️ Answer/Explanation
Detailed solution:
Planets orbit the Sun in paths that are elliptical, with the Sun located at one focus of the ellipse.
A galaxy is a massive collection of stars and does not orbit the Sun; red giants are stars, and moons orbit planets.
According to Kepler’s First Law, all planets move in elliptical orbits around the Sun, not perfect circles.
While a moon orbits a planet, it is the planet that travels around the Sun in this specific elliptical manner.
Therefore, a planet is the correct object described as rotating around the Sun with an elliptical orbit.
▶️ Answer/Explanation
Detailed solution:
The Sun produces energy through nuclear fusion, specifically the fusion of hydrogen nuclei into helium.
Fission, which involves splitting heavy nuclei, is the process used in nuclear power plants, not in stars like the Sun.
This fusion process releases vast amounts of energy across the entire electromagnetic spectrum, including visible light, ultraviolet, and infrared.
The statement correctly identifies both the type of nuclear reaction (fusion) and the broad production of electromagnetic radiation.
Options A, B, and C are incorrect because the Sun is not powered by fission and does not mainly create radio/microwaves.
Therefore, option D is the correct statement regarding the Sun’s energy source.
▶️ Answer/Explanation
Detailed solution:
The Hubble constant is given by \(H_0 = \frac{v}{d}\), where \(v\) is recession speed and \(d\) is distance.
Substituting the given values: \(H_0 = \frac{5.2 \times 10^3}{2.5 \times 10^{21}} = 2.08 \times 10^{-18} \text{ s}^{-1}\).
This matches option B (\(2.1 \times 10^{-18} \text{ s}^{-1}\)) when rounded appropriately.
The units are \( \text{s}^{-1} \) because km cancels out in the ratio.
This calculation directly applies the definition of the Hubble constant from the syllabus.