▶️ Answer/Explanation
Detailed solution:
To find the length of the feather, we need to look at the positions of both ends on the ruler. The left end of the feather starts at the $10\text{ mm}$ (or $1\text{ cm}$) mark. The right end of the feather aligns with the $29\text{ mm}$ (or $2.9\text{ cm}$) mark on the scale. To calculate the actual length, we subtract the starting position from the ending position: $29\text{ mm} – 10\text{ mm} = 19\text{ mm}$. Looking at the options provided, this calculation directly corresponds to $19\text{ mm}$. Therefore, the correct length of the feather is $19\text{ mm}$, which is Option A.
▶️ Answer/Explanation
Detailed solution:
By observing the diagram, it is clear that the spring holding object Y has a significantly larger extension compared to the spring holding object X.
Since the springs are identical, a greater extension indicates that a larger downward force, or weight, is being applied by object Y ($W_Y$ > $W_X$).
Weight and mass are directly proportional as shown by the formula $W = mg$, where $g$ is the gravitational field strength.
Because object Y has a greater weight and both objects are in the same gravitational field, object Y must also have a greater mass than object X ($m_Y$ > $m_X$).
Therefore, both the mass and the weight of the two objects are different, making Option D the correct choice.
▶️ Answer/Explanation
Detailed solution:
To find the density of the oil, we first need to determine its mass by subtracting the mass of the empty bottle from the mass of the full bottle.
From the diagram, the mass of the oil is $700 \text{ g} – 100 \text{ g} = 600 \text{ g}$.
The volume of the oil is given in the question as $750 \text{ cm}^3$.
Using the density formula, $\text{density} = \frac{\text{mass}}{\text{volume}}$, we substitute our values: $\text{density} = \frac{600 \text{ g}}{750 \text{ cm}^3}$.
By calculating this quotient, we get $0.80 \text{ g/cm}^3$.
Therefore, the density of the oil matches Option A.
▶️ Answer/Explanation
Detailed solution:
To find the weight of the object, we first need to calculate the extension produced in the spring.
The extension $x$ is the difference between the final length and the original unstretched length: $16.4\text{ cm} – 15.0\text{ cm} = 1.4\text{ cm}$.
Next, we look at the provided extension–load graph to find what load corresponds to an extension of $1.4\text{ cm}$.
By locating $1.4\text{ cm}$ on the vertical (extension) axis and tracing across to the line, we drop down to the horizontal (load) axis.
The graph shows that an extension of $1.4\text{ cm}$ corresponds exactly to a load of $3.5\text{ N}$.
Therefore, the weight of the unknown object is $3.5\text{ N}$, making Option C the correct choice.
▶️ Answer/Explanation
Detailed solution:
To find the centre of gravity of an irregular card, we use the plumb-line method which relies on static equilibrium rather than timing.
The pin is essential to act as a pivot so the card can hang freely, while the weight on a thin string (the plumb-line) creates a vertical reference line.
We use the pencil to mark the path of the string on the card from different hanging points.
The intersection of these marked lines identifies the exact position of the centre of gravity.
Since the experiment does not involve measuring the rate of motion or period of oscillation, a stop-watch is completely unnecessary for this procedure.
Therefore, Option D is the correct choice as it is the only tool listed that serves no purpose in locating the center of mass.
▶️ Answer/Explanation
Detailed solution:
When a cyclist is moving, the bicycle and the rider possess energy in the kinetic energy store due to their motion.
Applying the brakes creates friction between the brake pads and the wheels, which does work to slow down the bicycle.
As the bicycle decelerates and eventually stops, the energy in its kinetic energy store decreases.
This “lost” kinetic energy does not disappear but is transferred into the thermal energy store of the brakes and the surroundings.
Therefore, the kinetic energy store of the bicycle decreases while the thermal energy store of the brakes increases, making Option B correct.
▶️ Answer/Explanation
Detailed solution:
To find the power required, we first need to calculate the work done by the man. Work is defined as force multiplied by the distance moved in the direction of the force, so we have $W = F \times d = 40 \text{ N} \times 4.0 \text{ m} = 160 \text{ J}$.
Power is the rate at which work is done, which we calculate using the formula $P = \frac{W}{t}$.
Substituting our values, we get $P = \frac{160 \text{ J}}{3.0 \text{ s}}$, which equals approximately $53.33 \text{ W}$.
When we look at the given options, $53 \text{ W}$ is the closest value provided.
Therefore, the correct choice is Option C.
▶️ Answer/Explanation
Detailed solution:
The pressure difference in a fluid depends on the change in depth, calculated by the formula $\Delta P = \rho g \Delta h$.
Since the density $\rho$ and gravitational field strength $g$ are constant for all submarines, we only need to compare the change in depth ($\Delta h$) for each.
Submarines P and Q both move through a depth difference of $10\text{ m}$ ($20 – 10 = 10$ and $30 – 20 = 10$), so they must experience the same pressure difference.
Similarly, submarines R and S move through a depth difference of $20\text{ m}$ ($30 – 10 = 20$ and $40 – 20 = 20$), meaning they also share an identical, albeit larger, pressure change.
Looking at the table, Row A correctly identifies that P and Q have the same change, while R and S have the same change.
This confirms that the magnitude of pressure change is solely a function of the vertical distance traveled within the fluid.
▶️ Answer/Explanation
Detailed solution:
A change of state refers to the physical transformation of a substance from one form to another, such as liquid to gas.
Boiling is a process where a liquid turns into a gas throughout the bulk of the liquid at a specific temperature.
Evaporation is also a process where a liquid turns into a gas, but it occurs only at the surface and can happen at any temperature.
Since both “boiling” and “evaporation” describe the transition from the liquid state to the gaseous state, they identify the same change of state.
In contrast, solidification refers to liquid to solid, and condensation refers to gas to liquid, making Option B the correct choice.
▶️ Answer/Explanation
Detailed solution:
The random, zigzag motion of the smoke particles shown in Diagram 2 is a classic demonstration of Brownian motion.
This phenomenon occurs because the relatively large smoke particles are being constantly bombarded by much smaller, rapidly moving air molecules.
Since these air molecules move in random directions and at high speeds, they hit the smoke particles unevenly from all sides.
These microscopic collisions provide enough force to change the direction of the smoke particle, causing the erratic path we see under the microscope.
Therefore, the observed movement is direct evidence of the kinetic particle model of matter, specifically that air consists of tiny particles in constant motion.
▶️ Answer/Explanation
Detailed solution:
To convert between the Celsius and Kelvin scales, we use the relationship defined by absolute zero, where $0\text{ K}$ is equal to $-273.15^\circ\text{C}$.
In most physics problems at this level, we use the rounded constant of $273$ for simplicity in calculations.
The formula for the conversion is expressed as $T(\text{K}) = \theta(^\circ\text{C}) + 273$, meaning the Kelvin temperature is always higher than the Celsius value.
For example, the freezing point of water is $0^\circ\text{C}$, which corresponds to $273\text{ K}$ on the absolute scale.
Therefore, to find the temperature in kelvin, you simply need to add $273$ to the given Celsius value, making Option A the correct choice.
▶️ Answer/Explanation
Detailed solution:
When the air inside the cylinder is heated, the kinetic energy of the gas particles increases, leading to a rise in temperature.
Since the piston is described as “frictionless” and is free to move, it will shift outward as the gas expands to maintain a balance with the external atmospheric pressure.
This outward movement directly indicates that the volume of the gas is increasing.
Because the piston moves freely to equalize the internal and external forces, the process occurs at a constant pressure.
Therefore, as heat is added, both the temperature and the volume increase while the pressure remains unchanged, making Option A the correct choice.
▶️ Answer/Explanation
Detailed solution:
When the temperature of a substance increases, the average kinetic energy of its constituent particles also increases.
The internal energy of a system is defined as the sum of the microscopic kinetic energy and potential energy of all its particles.
Since temperature is a direct measure of the average kinetic energy, raising the temperature of the copper block necessarily boosts its total internal energy.
The number of atoms and the melting point are intrinsic properties that do not change simply by heating the solid.
Additionally, since objects typically expand when heated, the volume increases while mass stays constant, leading to a decrease in density, not an increase.
▶️ Answer/Explanation
Detailed solution:
The process described involves molecules gaining enough kinetic energy to overcome the attractive forces of their neighbors and leaving the liquid phase.
Since this specifically mentions molecules escaping from the surface rather than throughout the bulk of the liquid, it characterizes evaporation rather than boiling.
When these high-energy molecules leave, the average kinetic energy of the remaining molecules in the liquid decreases.
Because temperature is a direct measure of the average kinetic energy, this loss results in the cooling of the liquid.
This “evaporative cooling” is a fundamental thermal process, making Option D the correct answer.
▶️ Answer/Explanation
Detailed solution:
Radiation is the only method of heat transfer that can travel through a vacuum, as it does not require a medium like a solid, liquid, or gas.
Between the Sun and the Earth, there is mostly empty space (a vacuum), so conduction and convection cannot happen at all.
The energy travels across this space in the form of electromagnetic waves, specifically infrared radiation and visible light.
In the other options, the transfer depends on particle movement: a stove relies on conduction through the pan, while convection heaters and thermal currents rely on the movement of air or water molecules.
Therefore, the Sun’s energy reaching Earth is the classic example of radiation being the primary transfer method.
▶️ Answer/Explanation
Detailed solution:
To find the correct values, we need to look closely at how wavelength and amplitude are defined on a wave diagram.
The wavelength is the horizontal distance between two consecutive identical points, such as from one crest to the next; in the diagram, this corresponds to distance $x$.
The amplitude is the maximum displacement from the equilibrium (center) position to a crest or trough, which is shown as distance $z$.
Notice that $w$ represents the distance for two full wavelengths, and $y$ represents the total height from crest to trough (double the amplitude).
Therefore, the wavelength is $x$ and the amplitude is $z$, which matches the data provided in row D.
▶️ Answer/Explanation
Detailed solution:
Seismic P-waves, or primary waves, are longitudinal waves, which means the particles of the medium vibrate parallel to the direction of wave travel.
Unlike S-waves, which are slower and only travel through solids, P-waves are the fastest seismic waves and can travel through both solids and liquids, including the Earth’s liquid outer core.
Looking at the table, Row A correctly identifies P-waves as longitudinal waves that can pass through both states of matter.
This ability to travel through liquids is why P-waves are detected on the opposite side of the Earth after an earthquake, even after passing through the core.
Therefore, Option A is the only choice that accurately describes the fundamental nature and behavior of a P-wave.
▶️ Answer/Explanation
Detailed solution:
Diffraction is the physical phenomenon where waves spread out or bend as they pass through a narrow gap or travel around the edge of an obstacle.
Looking at the options, Diagram A shows reflection, Diagram B shows refraction through a medium, and Diagram C shows the dispersion of light into its constituent colors.
In Diagram D, we clearly see plane waves passing through a small opening and emerging as circular wavefronts that spread into the region beyond the barrier.
This spreading effect is the characteristic signature of diffraction, which is most noticeable when the size of the gap is similar to the wavelength of the wave.
Therefore, Diagram D is the only one that correctly illustrates the process of diffraction.
▶️ Answer/Explanation
Detailed solution:
When light travels from a more dense medium (glass) to a less dense medium (air), it bends away from the normal.
The critical angle is the specific angle of incidence for which the angle of refraction is exactly $90^\circ$.
If the angle of incidence is increased further so that it becomes greater than this critical angle, refraction can no longer occur.
At this point, all the light is reflected back into the denser medium, a phenomenon known as Total Internal Reflection (TIR).
Therefore, no light exits into the air, and we only see a reflected ray inside the glass, making Option D the correct choice.
▶️ Answer/Explanation
Detailed solution:
In the visible light spectrum, blue light has a higher energy than red light, which means it must have a higher frequency and a shorter wavelength.
Since the red light frequency is $430 \times 10^{12}$ Hz, we look for a frequency value greater than this, which points us toward $670 \times 10^{12}$ Hz.
Similarly, because the wavelength of red light is $700 \times 10^{-9}$ m, the wavelength for blue light must be smaller, making $450 \times 10^{-9}$ m the logical choice.
We can also verify this using the wave equation $v = f \lambda$, where the speed of light is constant; as frequency increases, wavelength must decrease.
Therefore, the only set of values that correctly represents the properties of blue light relative to red light is found in Option C.
▶️ Answer/Explanation
Detailed solution:
Infrared radiation is primarily associated with the transfer of thermal energy, which makes it highly effective for applications like remote controls and specialized heating.
In the context of the given options, using infrared for “intruder alarms” is a very common application, as these systems detect the heat emitted by a person’s body.
Regarding the biological risks, because infrared waves carry heat, overexposure can lead to physical damage of the tissue.
Specifically, intense or prolonged exposure to infrared radiation is known to cause skin burns due to the rapid heating of the skin surface.
Therefore, Row B correctly identifies both a practical technological use and a recognized health hazard associated with this part of the electromagnetic spectrum.
▶️ Answer/Explanation
Detailed solution:
To solve this, we first need to recall that a healthy human ear can typically hear frequencies ranging from $20\text{ Hz}$ to $20,000\text{ Hz}$ ($20\text{ kHz}$).
Looking at the table, we evaluate which animal’s range aligns closest with these two boundary values.
The chicken and the elephant have much lower upper limits, while the bat and moth hear far into the ultrasonic range, well beyond $20\text{ kHz}$.
The chimpanzee, with a range of $28\text{ Hz}$ to $28,000\text{ Hz}$, shows the most significant overlap and proximity to the human hearing spectrum.
Therefore, the chimpanzee (Option D) is the most similar to a human in terms of auditory frequency response.
▶️ Answer/Explanation
Detailed solution:
Sound waves are categorized as longitudinal waves because the particles of the medium vibrate parallel to the direction of wave travel.
The human ear has a specific audible range, typically between $20$ Hz and $20\,000$ Hz.
Any sound wave with a frequency higher than the upper limit of human hearing, which is $20\,000$ Hz (or $20$ kHz), is defined as ultrasound.
In contrast, frequencies below $20$ Hz are known as infrasound.
Since ultrasound is still a form of sound, it must be longitudinal, making the combination of “longitudinal” and “greater than $20\,000$ Hz” the correct physical description.
▶️ Answer/Explanation
Detailed solution:
When we look at the magnetic field around a bar magnet, the field lines represent the direction that a North pole of a small compass would point.
By convention, these field lines always emerge from the North ($N$) pole and loop around to enter the South ($S$) pole of the magnet.
The lines should be most dense at the poles where the magnetic field is strongest and should never cross each other.
In diagram A, the arrows correctly show the path moving away from the North and toward the South, following a smooth, continuous loop.
Diagrams B, C, and D are incorrect because the arrows either point the wrong way or show field lines entering and leaving the wrong poles.
▶️ Answer/Explanation
Detailed solution:
An electrical conductor is a material that allows electric charges to flow through it easily due to the presence of free electrons.
Copper is a metal, and metals are generally excellent conductors because their outermost electrons are delocalized and can move freely throughout the structure.
On the other hand, materials like glass, rubber, and wood are classified as insulators.
Insulators have tightly bound electrons that do not move easily, which prevents the flow of an electric current under normal conditions.
Therefore, copper is the only material among the choices that is used widely in electrical wiring because of its high conductivity.
This makes Option B the correct answer.
▶️ Answer/Explanation
Detailed solution:
Electric current is fundamentally defined as the rate of flow of charge, specifically the flow of electrons through a conductor.
To measure how much charge passes through a specific component like a resistor, we need the current to flow directly through the measuring device.
An ammeter has very low resistance and must always be placed in series with the component to ensure it captures the full flow of current.
Looking at the provided table, Option B correctly identifies current as the flow of charge and states that the ammeter should be in series.
This setup allows for an accurate reading without significantly altering the total resistance of the circuit branch.
Therefore, Option B is the scientifically correct choice for describing current and its measurement technique.
▶️ Answer/Explanation
Detailed solution:
Potential difference, often abbreviated as p.d., represents the amount of electrical work done or energy transferred per unit charge between two points in a circuit.
When we look at the standard SI units for electrical quantities, the ampere is used to measure current, while the joule is the unit for energy and work.
The ohm is specifically designated for measuring electrical resistance within a component or wire.
The volt ($V$) is the standard unit specifically used for potential difference and electromotive force.
Therefore, we measure the “voltage” or p.d. across components using a voltmeter, which provides readings in volts, making Option D the correct choice.
▶️ Answer/Explanation
Detailed solution:
To make the heater work, there must be a continuous closed loop for the electric current to flow from the power source through the heater and back.
Looking at the circuit, switch $S_{1}$ is located on the main wire near the battery, so it must be closed for any current to leave the source.
The heater is located on a specific parallel branch, and for current to reach it, switch $S_{4}$ must be closed as it is directly in series with the heater component.
Finally, switch $S_{2}$ must be closed to complete the return path to the negative terminal of the battery.
Switch $S_{3}$ is in a separate parallel branch containing a lamp, so it does not need to be closed for the heater to function; therefore, the required combination is $S_{1}$, $S_{2}$, and $S_{4}$.
▶️ Answer/Explanation
Detailed solution:
The earth wire is a safety feature designed to provide a low-resistance path for electricity to flow into the ground.
If a fault occurs and a live wire touches the metal casing of the appliance, the casing becomes “live” and dangerous to touch.
With an earth connection, the current flows safely through the earth wire instead of passing through a person who touches the device.
This high current flow typically causes the fuse to blow or the circuit breaker to trip, cutting off the power completely.
Therefore, the primary function of the earth connection is to prevent the user from receiving a fatal electric shock.
Options A, B, and C describe circuit completion or maintenance issues that are not the purpose of an earth wire.
▶️ Answer/Explanation
Detailed solution:
According to Faraday’s law of electromagnetic induction, the magnitude of the induced e.m.f. is directly proportional to the rate at which the magnetic flux linkage changes.
Factors like the speed of the magnet, the strength of the magnetic field, and the number of turns in the coil all change how quickly or intensely the flux lines are cut, thereby altering the voltage level.
The polarity of the magnet (whether the North or South pole enters first) only determines the direction of the induced current and the sign of the e.m.f., not its size.
If you flip the magnet, the needle on the voltmeter will simply deflect in the opposite direction, but the numerical value (magnitude) will remain exactly the same.
Therefore, the polarity has no effect on the magnitude of the induced e.m.f., making Option B the correct answer.
▶️ Answer/Explanation
Detailed solution:
To build a functioning d.c. motor, you need the fundamental components that allow for the motor effect to occur.
The motor effect requires a current-carrying conductor placed within a magnetic field to generate a force.
The battery provides the necessary direct current ($d.c.$) source, while the coil of wire acts as the conductor that will experience the force.
Magnets are essential to provide the external magnetic field that interacts with the current in the coil.
While meters like ammeters or voltmeters are useful for monitoring the circuit, they are not strictly required for the motor to actually spin.
Therefore, the combination of a battery, coil, and magnets represents the absolute minimum set of components needed for the motor to operate.
▶️ Answer/Explanation
Detailed solution:
To solve this, we need to look at the basic structure of an atom and the charges of its constituent particles.
The nucleus is located at the center of the atom and contains protons, which have a positive ($+$) charge, and neutrons, which have no charge ($0$).
Because the nucleus contains these positive protons, the overall charge of the nucleus itself must be positive.
Orbiting around this central nucleus are the electrons, which carry a negative ($-$) charge.
Comparing these facts to the table, Row C correctly identifies that the orbiting particles are electrons and the charge on the nucleus is positive.
This matches the standard Rutherford-Bohr model of atomic structure used in physics.
▶️ Answer/Explanation
Detailed solution:
To solve this, we need to look at the fundamental properties of subatomic particles found in the nucleus.
A proton is a positively charged particle, and by convention, its relative charge is assigned a value of $+1$.
On the other hand, a neutron, as its name suggests, is electrically neutral, meaning it carries no net charge, represented as $0$.
Comparing these facts with the table provided, we look for the row where the proton is positive and the neutron is zero.
This corresponds exactly to the data in row B, making it the correct identification for these nuclear particles.
This basic understanding of atomic structure is essential for explaining how atoms stay balanced and how radioactive decay occurs.
▶️ Answer/Explanation
Detailed solution:
When a radioactive nucleus undergoes alpha ($\alpha$) decay, it ejects an alpha particle, which consists of $2$ protons and $2$ neutrons.
Since protons determine the identity of an element, losing $2$ protons means the atomic number decreases by $2$.
Because the proton number changes, the atom transforms into an entirely different element rather than remaining an isotope of radon.
This process results in a new nucleus that has a lower proton number and a lower mass number than the original atom.
Therefore, the identity of the element changes to one located two places earlier in the periodic table, making option D the correct choice.
▶️ Answer/Explanation
Detailed solution:
In the nuclide notation $_{Z}^{A}\text{X}$, $A$ represents the nucleon number (mass number) and $Z$ represents the proton number (atomic number).
For $_{38}^{90}\text{Sr}$, the nucleon number $A = 90$ and the proton number $Z = 38$.
The number of neutrons $N$ is calculated using the formula $N = A – Z$.
Substituting the values gives $N = 90 – 38 = 52$ neutrons.
The nucleus contains only protons and neutrons, so statement C is incorrect as electrons are not in the nucleus.
Therefore, statement B is the only correct description of the strontium-90 nucleus.
▶️ Answer/Explanation
Detailed solution:
Radioactive sources emit various types of radiation, such as alpha particles, beta particles, and gamma rays, which have different penetrating powers.
While alpha and beta particles can be stopped by thin layers of material like paper or aluminium, gamma radiation is highly energetic and requires a very dense material to be effectively attenuated.
Lead is the ideal choice for lining storage boxes because its high density and high atomic number provide a high probability of absorbing these gamma rays.
Materials like plastic or paper are far too thin and low-density to offer any significant protection against the hazardous emissions of a radioactive source.
Therefore, using lead ensures that the radiation is contained within the box, protecting the surrounding environment and individuals from exposure.
This makes Option B the standard safety requirement for storing radioactive materials.
▶️ Answer/Explanation
Detailed solution:
The Earth’s movement in space involves two main motions: rotation on its own axis and revolution around the Sun.
The rotation of the Earth on its axis occurs every $24$ hours and is responsible for the daily cycle of day and night as well as the Sun’s apparent motion across the sky.
In contrast, the Earth takes approximately $365$ days to complete one full orbit, or revolution, around the Sun.
This annual revolution, combined with the fixed tilt of the Earth’s axis, leads to changes in the intensity and duration of sunlight received at different latitudes throughout the year.
Consequently, this $365$-day orbital period is the fundamental reason behind the periodic nature of the seasons.
Therefore, Option C is the correct explanation for what this yearly cycle enables us to understand.
▶️ Answer/Explanation
Detailed solution:
To find the time light takes to travel between the two planets, we first need to determine the minimum distance between them.
The planets are closest to each other when they are aligned on the same side of the Sun; this distance is the difference between their orbital radii: $150 \times 10^6 \text{ km} – 110 \times 10^6 \text{ km} = 40 \times 10^6 \text{ km}$.
Using the formula $\text{time} = \frac{\text{distance}}{\text{speed}}$, we substitute the values: $t = \frac{40 \times 10^6 \text{ km}}{0.30 \times 10^6 \text{ km/s}}$.
The $10^6$ terms cancel out, leaving us with $t = \frac{40}{0.30}$, which equals approximately $133.33$ seconds.
Looking at the given options, $130 \text{ s}$ is the closest value provided.
Therefore, the light takes about $130 \text{ s}$ to travel from Venus to Earth at their closest approach.
▶️ Answer/Explanation
Detailed solution:
The Sun emits a wide spectrum of electromagnetic radiation, but the vast majority of its energy reaches Earth in three primary forms.
Visible light is the most obvious, providing the illumination we see during the day.
Infrared radiation is what we feel as heat, making up about $49\%$ of the solar energy reaching the surface.
Ultraviolet (UV) radiation, while comprising a smaller percentage, is responsible for effects like sunburn and is highly energetic.
While the Sun does emit radio waves and X-rays, their intensity is negligible compared to the massive output of infrared, visible, and ultraviolet light, making Option B the correct choice.
▶️ Answer/Explanation
Detailed solution:
Even though the word “year” appears in the name, a light-year is actually a unit of distance, not time.
It represents the total distance that a beam of light travels through the vacuum of space in one Julian year ($365.25$ days).
Since light moves at an incredible speed of approximately $3 \times 10^{8}$ m/s, it covers about $9.46$ trillion kilometers in that time.
This unit is used by astronomers to measure the vast gaps between stars and galaxies where kilometers or miles would be too small to be practical.
Therefore, Option C is the correct definition, as it correctly identifies it as a measure of distance over a specific duration.