▶️ Answer/Explanation
Detailed solution:
The volume of an irregularly shaped stone is found by the displacement method using a measuring cylinder with water.
The stone is submerged, and the rise in water level equals the stone’s volume; a ruler is not needed for irregular shapes.
Option A includes an unnecessary ruler, while options C and D lack water for displacement measurement.
Therefore, a measuring cylinder containing water only is the essential apparatus for this procedure.
Hence, option B is the correct choice.
▶️ Answer/Explanation
Detailed solution:
A vector quantity has both magnitude and direction, whereas a scalar quantity has only magnitude.
Energy, mass, and temperature are all scalar quantities as they do not involve direction.
Electric field strength is defined as the force per unit positive charge and acts in a specific direction.
The syllabus explicitly lists electric field strength as one of the vector quantities to be known.
Therefore, only option A possesses the characteristics of a vector quantity.
Consequently, electric field strength is the correct answer.
▶️ Answer/Explanation
Detailed solution:
Convert distance to metres: \(2.4 \text{ km} = 2400 \text{ m}\) and time to seconds: \(12 \text{ min} = 720 \text{ s}\).
Use the formula for average speed: \(v = \frac{s}{t} = \frac{2400}{720} \approx 3.33 \text{ m/s}\).
This matches option B. Options A, C, and D result from incorrect unit conversions or calculation errors.
Therefore, the average speed of the athlete is \(3.3 \text{ m/s}\).
▶️ Answer/Explanation
Detailed solution:
Acceleration is found from the gradient (slope) of a speed-time graph; steeper slopes indicate greater acceleration or deceleration.
The greatest acceleration occurs where the graph rises most steeply, which is from 0 s to 20 s (gradient = (20–0)/(20–0) = 1.0 m/s²).
Deceleration is negative acceleration, shown where the graph slopes downward; the steepest downward slope is from 30 s to 40 s (gradient = (0–20)/(40–30) = –2.0 m/s²).
Comparing the given table options, row D correctly identifies the intervals 0–20 s for greatest acceleration and 30–40 s for greatest deceleration.
Thus, based on gradient analysis, the car’s motion matches the values in option D.
▶️ Answer/Explanation
Detailed solution:
Gravitational field strength \(g\) is defined as the gravitational force per unit mass, given by \(g = \frac{W}{m}\).
From Newton’s second law, this ratio is dimensionally equivalent to acceleration, specifically the acceleration of free fall.
Options A and B incorrectly rearrange the relationship between mass, weight, and \(g\).
Option C incorrectly describes mass per unit force, which is the inverse of the correct definition.
Therefore, stating that \(g\) is equal to the acceleration of free fall is the only correct statement.
▶️ Answer/Explanation
Detailed solution:
Mass is the measure of the quantity of matter in an object and remains constant regardless of applied forces.
Forces can alter an object’s shape through compression or extension, change its speed via acceleration, and even affect its volume.
Therefore, while shape, speed, and volume are variable under force application, mass is an intrinsic property that does not change.
Consequently, option A correctly identifies the property that forces cannot alter.
▶️ Answer/Explanation
Detailed solution:
By the principle of conservation of momentum, total momentum before impact equals total momentum after impact.
Momentum before = (0.10 × 600) + (1.9 × 0) = 60 kg m/s. Combined mass after = 0.10 + 1.9 = 2.0 kg.
Using p = mv, 60 = 2.0 × v, so v = 30 m/s. This is a perfectly inelastic collision as the ball embeds in the block.
The other options are incorrect: 32 m/s and 130 m/s do not satisfy momentum conservation, and 60 m/s is the initial speed of the ball only.
Thus, the speed immediately after impact is 30 m/s, matching option A.
▶️ Answer/Explanation
Detailed solution:
Total pressure = atmospheric pressure + pressure due to water column (ρgh).
Given maximum total pressure is 2.1 MPa = 2.1 × 10⁶ Pa.
Therefore, ρgh = 2.1 × 10⁶ Pa – 1.01 × 10⁵ Pa = 1.999 × 10⁶ Pa.
Solving for h: h = P / (ρg) = 1.999 × 10⁶ / (1000 × 9.8) ≈ 204 m.
Thus, the maximum safe depth for the object is 204 m, which corresponds to option B.
▶️ Answer/Explanation
Detailed solution:
When a solid metal melts, it changes state to a liquid without any change in particle size.
In the solid state, particles are arranged in a fixed pattern and can only vibrate about fixed positions.
Upon melting, the particles gain enough energy to break free from their fixed arrangement and begin to slide or move around each other.
This movement allows the liquid to flow and take the shape of its container, while the particles remain close together.
Therefore, the correct description of the change in particle behaviour during melting is that they move around each other.
▶️ Answer/Explanation
Detailed solution:
Brownian motion is the random, unpredictable movement of microscopic particles suspended in a fluid, caused by uneven collisions with fast-moving fluid molecules.
Statement 1 is incorrect because the particles do not follow a uniform curved path; their motion is erratic and changes direction constantly.
Statement 2 is correct as the defining characteristic of Brownian motion is its randomness, with no set pattern or preferred direction.
Statement 3 is incorrect because the particles do not move in the same direction; their individual motions are independent and chaotic.
Therefore, only statement 2 correctly describes Brownian motion, making option D the correct answer.
▶️ Answer/Explanation
Detailed solution:
At constant temperature, the average speed (and thus velocity) of the gas particles remains unchanged.
Decreasing the volume reduces the distance particles travel between collisions with the walls.
This shorter travel distance means each particle collides with the walls more frequently per unit time.
Since the velocity is unchanged but the collision frequency increases, option D is correct.
This increased collision rate results in a higher pressure exerted on the cylinder walls.
▶️ Answer/Explanation
Detailed solution:
For a fixed mass of gas at constant temperature, the relationship between pressure (p) and volume (V) is given by Boyle’s Law: pV = constant.
This means that pressure is inversely proportional to volume, producing a hyperbolic curve when plotted on a p–V graph.
As the volume decreases, the pressure increases, and the curve does not touch either axis since neither pressure nor volume can be zero.
The graph in option B correctly shows this inverse proportionality with a smooth curve approaching both axes asymptotically.
Therefore, the correct graphical representation for the compression of the gas at constant temperature is option B.
▶️ Answer/Explanation
Detailed solution:
When a thermometer is placed in hot water, thermal energy is transferred to the liquid inside, increasing the kinetic energy of its particles.
This causes the particles to move slightly further apart on average, resulting in an increase in the volume of the liquid.
This phenomenon is known as thermal expansion, and the expanding liquid has nowhere to go but up the narrow bore of the thermometer tube.
Therefore, the rise in the liquid level is a direct observation of the liquid expanding due to the increase in temperature.
Option C is the correct scientific explanation for this everyday observation.
▶️ Answer/Explanation
Detailed solution:
During melting, ice absorbs thermal energy (latent heat of fusion) to overcome the intermolecular bonds holding the solid structure together.
This energy input does not increase the kinetic energy of the particles, so the temperature remains constant at 0°C until all ice has melted.
Options B and D are incorrect because temperature does not rise during the phase change.
Options C and D are incorrect because energy is absorbed (endothermic), not released (exothermic).
Therefore, the correct description is that energy is absorbed while the temperature stays constant, making A the right choice.
▶️ Answer/Explanation
Detailed solution:
Evaporation occurs when more energetic particles escape from the liquid surface.
Increasing the surface area allows more particles to be near the surface and potentially escape.
Blowing air across the surface removes the vapor particles just above the liquid, preventing them from returning.
Both actions increase the rate at which liquid turns into vapor, matching the combination described in row D.
Therefore, D is the correct explanation for the observed increase in evaporation rate.
▶️ Answer/Explanation
Detailed solution:
Thermal conduction in solids occurs via lattice vibrations and, in metals, the movement of free electrons.
Material R is a solid containing free electrons, which indicates it is a metal and an excellent thermal conductor.
Material P is a solid but lacks free electrons, so it conducts heat less effectively than R.
Materials Q (liquid) and S (gas) generally have particles spaced farther apart, making them poor conductors compared to solids.
Since free electrons significantly enhance heat transfer, conduction is best in R, making option C the correct comparison.
▶️ Answer/Explanation
Detailed solution:
The wave equation relates speed (v), frequency (f), and wavelength (λ) as v = f λ.
Rearranging gives λ = v / f = (10 km/s) / (5.0 Hz) = 2.0 km.
This calculation applies to all waves, including seismic waves, which transfer energy through the Earth.
The unit of wavelength is a distance, and using consistent units (km and s) yields the answer in km.
Thus, the seismic wave has a wavelength of 2.0 km, making option C correct.
▶️ Answer/Explanation
Detailed solution:
Diffraction is most significant when the wavelength is comparable to or larger than the obstacle or gap size.
For diffraction through a gap, a long wavelength spreads out more compared to a narrow gap.
For diffraction at an edge, a long wavelength also bends around the barrier more noticeably.
Thus, in both cases—going through a gap or passing an edge—a long wavelength produces the greatest diffraction.
Option D correctly identifies long wavelength for both scenarios, consistent with wave behavior principles.
▶️ Answer/Explanation
Detailed solution:
A plane mirror produces an image that is laterally inverted, meaning left and right are reversed.
If the boy sees a normal ‘R’ in the mirror, the actual card must show the laterally inverted version of that letter.
Looking at the options, the shape in B represents the mirror image of a correctly oriented ‘R’.
When the card in option B is reflected, the lateral inversion in the mirror will flip it back to appear as a standard ‘R’.
Therefore, the printed letter on the card must be the one shown in option B to produce the observed image.
▶️ Answer/Explanation
Detailed solution:
The refractive index \(n\) relates the speed of light in vacuum \(c\) to the speed in the medium \(v\): \(n = c / v\).
From the diagram, using Snell’s law \(n = \sin i / \sin r = \sin 60^\circ / \sin 34^\circ \approx 0.866 / 0.559 \approx 1.55\).
Using \(c = 3.0 \times 10^8 \, \text{m/s}\), we find \(v = c / n = (3.0 \times 10^8) / 1.55 \approx 1.94 \times 10^8 \, \text{m/s}\).
This value is closest to \(2.0 \times 10^8 \, \text{m/s}\), making option A the correct answer.
The calculation uses the angles measured from the normal and the known speed of light in air/vacuum.
Therefore, the speed of light in the glass is approximately \(2.0 \times 10^8 \, \text{m/s}\).
▶️ Answer/Explanation
Detailed solution:
For a converging lens to act as a magnifying glass, the object must be placed between the lens and its principal focus.
This produces a virtual, upright, and magnified image on the same side of the lens as the object.
The virtual image appears further away from the lens than the object, typically at the near point of the eye.
Options B and C are incorrect because a magnifying glass produces a virtual and upright image, not a real or inverted one.
Option D is incorrect because an object at the principal focus forms an image at infinity, not a magnified viewable image.
Therefore, option A is the only correct statement.
▶️ Answer/Explanation
Detailed solution:
The visible spectrum in order of increasing wavelength is violet, indigo, blue, green, yellow, orange, red.
Option C shows indigo to green to red, which correctly follows the order of increasing wavelength.
Option A is incorrect as red has a longer wavelength than yellow and blue.
Option B is wrong because violet has the shortest wavelength, not longer than orange and green.
Option D lists blue to green to violet, which is decreasing wavelength, not increasing.
Therefore, option C accurately represents a sequence from shorter to longer wavelength.
▶️ Answer/Explanation
Detailed solution:
All electromagnetic waves travel at the same speed in a vacuum (\(3.0 \times 10^{8} \mathrm{~m/s}\)), so speed does not change.
The order shown (visible → ultraviolet → X-rays) represents increasing frequency and decreasing wavelength.
Therefore, only frequency increases in magnitude from left to right across the list.
Options involving speed changes are incorrect because speed is constant for all EM waves in a vacuum.
Thus, option B is the correct choice.
▶️ Answer/Explanation
Detailed solution:
Sound travels fastest in solids due to closely packed particles, slower in liquids, and slowest in gases.
At room temperature, typical speeds are approximately 5000 m/s in steel, 1500 m/s in water, and 330 m/s in air.
Row A correctly reflects this decreasing order: 5000 m/s in steel, 1500 m/s in water, and 330 m/s in air.
Other rows either reverse the order or provide values inconsistent with standard experimental data.
Therefore, option A is the correct choice.
▶️ Answer/Explanation
Detailed solution:
A compass needle aligns with the direction of the magnetic field lines, pointing from the north pole to the south pole outside a magnet.
The compass on the left is near the north pole, so its N-pole is repelled and points away to the right.
The compass on the right is near the south pole, so its N-pole is attracted and points toward the left.
This results in both compass needles pointing horizontally outward from the center of the magnet.
Option B correctly shows both N-poles pointing away from the magnet’s north pole and toward its south pole.
Therefore, the needles follow the external magnetic field direction as described in Topic 4.1.
▶️ Answer/Explanation
Detailed solution:
Statement 1 is incorrect because a stationary electric charge experiences a force in an electric field, not a magnetic field.
Statement 2 is incorrect as the direction of a magnetic field is defined by the force on a north (N) pole, not a south (S) pole.
Statement 3 is correct because the spacing of magnetic field lines indicates the field’s relative strength; closer lines mean a stronger field.
Therefore, only statement 3 is correct, making option D the right choice.
▶️ Answer/Explanation
Detailed solution:
When a plastic rod is rubbed with a cloth, electrons are transferred from the rod to the cloth.
Since the rod loses negative charge (electrons), it becomes positively charged overall.
The negatively charged object attracts the rod because opposite charges attract.
Options A and B are incorrect as they suggest the rod gained electrons or became negative.
Option C is incorrect because gaining electrons would make the rod negative, not positive.
Thus, the rod is positively charged due to the loss of electrons, making D correct.
▶️ Answer/Explanation
Detailed solution:
Conventional current flows from the positive terminal to the negative terminal of the battery, while electrons flow in the opposite direction.
In option B, the arrow for conventional current I correctly points away from the positive terminal and toward the negative terminal around the circuit.
The arrow for electron flow correctly points away from the negative terminal, opposite to the direction of conventional current.
Other options either reverse one direction incorrectly or show both arrows flowing in the same direction, which is physically inaccurate.
Therefore, option B correctly represents both the conventional current direction and the actual electron flow in a d.c. circuit.
▶️ Answer/Explanation
Detailed solution:
Electromotive force (e.m.f.) is defined as the electrical work done (energy transferred) per unit charge.
Using the equation E = W / Q, the energy transferred W = E × Q.
Substituting the given values: W = 1.5 V × 6.0 C = 9.0 J.
The unit of energy is the joule (J), whereas the watt (W) is the unit of power.
Therefore, the energy transferred by the cell is 9.0 J, making option C the correct answer.
▶️ Answer/Explanation
Detailed solution:
Resistance is directly proportional to length and inversely proportional to cross-sectional area.
Doubling the length to \(2l\) multiplies the resistance by 2.
Halving the area to \(\frac{A}{2}\) also multiplies the resistance by 2.
The combined effect is a factor of \(2 \times 2 = 4\), resulting in a total resistance of \(4R\).
Thus, the new wire has four times the original resistance, making option D correct.
▶️ Answer/Explanation
Detailed solution:
Circuit 1 uses a thermistor; its resistance falls as temperature rises, allowing current to activate the relay when hot.
Circuit 2 uses an LDR; its resistance falls as light intensity increases, energizing the relay in bright conditions.
For both LEDs to light, circuit 1 needs high temperature (hot) and circuit 2 needs high light intensity (light).
Option B (hot and light) matches these required conditions, causing both relay coils to close their respective circuits.
In all other options, at least one sensor condition fails to energize the relay, leaving one LED off.
Thus, only the combination of hot and light satisfies the operational requirements for both circuits.
▶️ Answer/Explanation
Detailed solution:
For an ideal (100% efficient) transformer, the voltage ratio equals the turns ratio: \( V_p / V_s = N_p / N_s \).
Since power input equals power output, \( I_p V_p = I_s V_s \), which rearranges to \( I_p / I_s = V_s / V_p \).
Combining these gives \( I_p / I_s = N_s / N_p \), exactly matching the pair of equations in option A.
Option B incorrectly relates current ratio directly to turns ratio without inversion.
Therefore, option A is the only valid pair of equations for a 100% efficient transformer.
▶️ Answer/Explanation
Detailed solution:
A neutral atom must have an equal number of positive protons and negative electrons.
Diagram A shows this equality with six protons in the nucleus and six electrons in orbit, balancing the charge.
The other diagrams show imbalances, resulting in a net positive or negative charge (ions).
Therefore, only diagram A correctly represents the structure of a neutral atom.
▶️ Answer/Explanation
Detailed solution:
Nuclear fission involves a heavy, unstable nucleus splitting into two (or more) smaller, lighter nuclei.
Option A describes nuclear fusion, which is the process powering stars (also described in option C).
Option B describes the process of ionization, not a nuclear reaction involving changes in the nucleus itself.
During fission, the total mass of the products is slightly less than the original nucleus, with the mass defect released as energy.
Therefore, option D correctly defines the process of nuclear fission as the splitting of a nucleus.
▶️ Answer/Explanation
Detailed solution:
Using Fleming’s left-hand rule, the deflection shows X is negatively charged (beta), Y is positively charged (alpha), and Z is uncharged (gamma).
Alpha particles (Y) have the greatest mass and are the most strongly ionising, causing significant damage over a short range.
Therefore, Z is gamma radiation, which is weakly ionising, making option C the only correct statement.
Option A is wrong because X (beta) is negative; option B is wrong because Y (alpha) is positive.
Option D is incorrect as X (beta) has a much smaller mass than Y (alpha).
Thus, alpha radiation (Y) is correctly identified as the most strongly ionising among the three.
▶️ Answer/Explanation
Detailed solution:
Smoke detectors use alpha emitters (like Americium-241) because alpha particles are highly ionising but have low penetration, making them safe in a small enclosure.
Sterilising medical equipment requires gamma rays due to their strong penetrating power, which kills bacteria effectively throughout the object.
Controlling the thickness of paper in a factory uses beta emitters, as beta particles are partially absorbed by the material; variations in detected count rate adjust the rollers.
Therefore, the sequence Alpha emitter / Gamma emitter / Beta emitter in Row C is the only correct match for these three specific industrial and medical applications.
▶️ Answer/Explanation
Detailed solution:
Lead is a dense material used as shielding to absorb ionising nuclear radiation, preventing it from reaching people.
It does not alter the half-life of a radioactive source, as half-life is a fixed property of the isotope.
While alpha particles can be stopped by paper, lead is effective at absorbing more penetrating beta and gamma rays.
This safety precaution protects users by reducing exposure to harmful emissions from the stored source.
Therefore, option A correctly explains why lead boxes are used for storage.
▶️ Answer/Explanation
Detailed solution:
Using \(v = \frac{2\pi r}{T}\) with \(r = 1.5 \times 10^{11} \text{ m}\) and \(T = 365 \text{ days}\), the orbital circumference is \(2\pi(1.5 \times 10^{11}) \approx 9.42 \times 10^{11} \text{ m}\).
Converting to km gives \(9.42 \times 10^{8} \text{ km}\), and dividing by 365 days yields approximately \(2.58 \times 10^{6} \text{ km/day}\).
This matches option C, confirming that Earth’s orbital speed around the Sun is about \(2.6 \times 10^{6} \text{ km/day}\).
▶️ Answer/Explanation
Detailed solution:
A star begins as a protostar formed from collapsing interstellar gas and dust.
It becomes a stable star when inward gravitational force balances outward pressure from nuclear fusion.
After exhausting hydrogen fuel, it expands into a red giant, and if massive enough, ends in a supernova explosion.
Therefore, the correct sequence is protostar → stable star → red giant → supernova, corresponding to option B.
▶️ Answer/Explanation
Detailed solution:
A light-year is the distance light travels in a vacuum in one year, which is approximately \(9.5 \times 10^{15}\) metres.
This is calculated using the speed of light (\(3.0 \times 10^8 \mathrm{~m/s}\)) multiplied by the number of seconds in a year.
The syllabus specifically states that one light-year equals \(9.5 \times 10^{15} \mathrm{~m}\), not kilometres.
Options A and B give incorrect numerical values, and option D uses the wrong unit (km).
Therefore, option C is the correct distance in the appropriate SI unit of metres.