▶️ Answer/Explanation
Detailed solution:
In a speed–time graph, the gradient represents the acceleration $a$. A straight line indicates constant acceleration, while a curved line indicates changing acceleration.
Section $P$ is a horizontal line where $a = 0$, and section $S$ is a vertical line indicating an instantaneous stop (infinite deceleration), neither of which represents a gradual “change” in acceleration.
Sections $Q$ and $R$ are curved, meaning the gradient is constantly varying as the car speeds up and slows down.
Specifically, in $Q$, the gradient increases then decreases, and in $R$, the negative gradient becomes steeper.
Therefore, only sections $Q$ and $R$ show an acceleration that is changing over time.
▶️ Answer/Explanation
Detailed solution:
First, calculate the horizontal resultant force: $60\text{ kN} – 40\text{ kN} = 20\text{ kN}$ acting to the right.
Next, calculate the vertical resultant force: $120\text{ kN} – 60\text{ kN} = 60\text{ kN}$ acting upwards.
The overall resultant force vector has components $(20, 60)$, meaning it points both up and to the right.
Since the vertical component ($60\text{ kN}$) is three times larger than the horizontal component ($20\text{ kN}$), the direction must be steeply angled toward the vertical.
Arrow B correctly represents a vector pointing predominantly upwards with a slight rightward lean.
Therefore, arrow B is the direction of the resultant of the four forces.
▶️ Answer/Explanation
Detailed solution:
Since blocks X and Y have “identical dimensions,” they occupy the same amount of space, meaning their volumes are equal ($V_X = V_Y$).
The force meters measure weight in Newtons (N); the pointer for X is at $2.0\text{ N}$ and the pointer for Y is at $3.0\text{ N}$.
This indicates the weights are different ($W_X \neq W_Y$), likely due to the blocks being made of materials with different densities.
According to the formula $W = mg$, a higher weight on the same planet implies a higher mass for block Y.
Therefore, the only correct statement is that they have equal volumes but different weights.
This corresponds exactly to Option D.
▶️ Answer/Explanation
Detailed solution:
To find the density $\rho$ of an object, we use the formula $\rho = \frac{m}{V}$.
The mass $m$ of the gold necklace is measured using a balance.
Since a necklace is an irregularly shaped solid, its volume $V$ is determined by displacement.
This requires a measuring cylinder to find the volume of liquid displaced when the necklace is submerged.
A ruler is impractical for measuring the complex dimensions of a necklace, and temperature is irrelevant to this calculation.
Therefore, only a balance and a measuring cylinder are necessary, making Row C the correct choice.
▶️ Answer/Explanation
Detailed solution:
The spring constant $k$ is defined by the formula $F = kx$, where $x$ is the extension.
First, calculate the change in load: $\Delta F = 7.0\text{ N} – 2.0\text{ N} = 5.0\text{ N}$.
Next, calculate the change in length (extension): $\Delta x = 35\text{ cm} – 25\text{ cm} = 10\text{ cm}$.
The spring constant is the ratio of the change in force to the change in extension: $k = \frac{\Delta F}{\Delta x}$.
Substituting the values: $k = \frac{5.0\text{ N}}{10\text{ cm}} = 0.50\text{ N/cm}$.
This matches Option B.
▶️ Answer/Explanation
Detailed solution:
For an object to be in equilibrium, there must be no resultant force ($F_{net} = 0~N$) and no resultant moment.
In diagrams E and F, the forces are not aligned along the same line of action, creating a clockwise or anticlockwise moment that would cause the block to rotate.
In diagrams G and H, the two $2~N$ forces act in opposite directions along the same line of action.
This results in a net force of $2~N – 2~N = 0~N$ and zero turning effect.
Therefore, only blocks G and H satisfy the conditions for static equilibrium.
Consequently, option D is the correct choice as it identifies both G and H.
▶️ Answer/Explanation
Detailed solution:
Momentum is defined as the product of mass and velocity, $p = mv$, making statement D correct.
Impulse is defined as the product of force and the time interval, which equals the change in momentum, $F\Delta t = \Delta(mv)$, making statement B correct.
The principle of conservation of momentum states that total momentum remains constant in a closed system, making statement A correct.
Resultant force is actually the change in momentum per unit time, expressed as $F = \frac{\Delta p}{\Delta t}$.
Statement C incorrectly suggests force is the product of change in momentum and time ($F = \Delta p \times t$).
Therefore, statement C is the only incorrect statement in the list.
▶️ Answer/Explanation
Detailed solution:
The relationship between force, mass, and acceleration is given by Newton’s Second Law: $F = ma$.
Rearranging for acceleration, we get $a = \frac{F}{m}$, where $a$ represents the rate of change in motion.
Since the force $F$ is constant, the acceleration $a$ is inversely proportional to the mass $m$ ($a \propto \frac{1}{m}$).
Therefore, to produce a greater change in motion (larger acceleration), the mass of the ball must be decreased.
Options B, C, and D do not change the mass or the resulting acceleration when the force remains constant.
▶️ Answer/Explanation
Detailed solution:
Pressure is defined as the force applied per unit area, expressed by the formula $p = \frac{F}{A}$. Since both carts have the same weight, the downward force $F$ exerted on the ground is constant for both. The wide wheels have a larger surface area $A$ in contact with the soft ground compared to the narrow wheels. According to the relationship $p \propto \frac{1}{A}$, a larger contact area results in a lower pressure $p$ exerted on the surface. Because the wide wheels exert less pressure, they are less likely to compress the soil, meaning they sink less into the ground. Therefore, Row D correctly identifies the wide wheels and the reason as less pressure.
▶️ Answer/Explanation
Detailed solution:
In the kinetic particle model, gas particles are far apart with no fixed arrangement, while liquid particles are close together. Therefore, the separation in a gas is significantly greater than in a liquid. Temperature is a measure of the average kinetic energy ($E_{k} = \frac{1}{2}mv^{2}$) of the particles. Since the gas is “hot” and the liquid is “cool,” the gas particles possess higher kinetic energy and move at a faster speed. Consequently, the hot gas has both a larger particle separation and higher particle velocity compared to the cool liquid. This makes Row A the correct description.
▶️ Answer/Explanation
Detailed solution:
For a fixed mass of gas at a constant temperature, pressure and volume are inversely proportional, following Boyle’s Law: $p_1V_1 = p_2V_2$.
Given initial values are $p_1 = 200\text{ kPa}$ and $V_1 = 1.2\text{ m}^3$, and the final volume is $V_2 = 1.8\text{ m}^3$.
Rearranging the formula to solve for the new pressure: $p_2 = \frac{p_1V_1}{V_2}$.
Substituting the values: $p_2 = \frac{200 \times 1.2}{1.8} = \frac{240}{1.8}$.
Calculating the result gives $p_2 = 133.33\dots\text{ kPa}$.
Rounding to the nearest provided option, the new pressure is approximately $130\text{ kPa}$.
▶️ Answer/Explanation
Detailed solution:
Specific heat capacity $c$ is defined by the equation $c = \frac{\Delta E}{m\Delta\theta}$, where $\Delta E$ is the thermal energy transferred.
It represents the energy required to raise the temperature of $1~kg$ (unit mass) of a substance by $1^{\circ}C$.
Since solid P has a higher specific heat capacity than solid Q ($c_P > c_Q$), it requires more energy for the same mass and temperature change.
Options B and D are incorrect as they refer to melting, which involves latent heat rather than specific heat capacity.
Therefore, statement C correctly identifies that more energy is needed for solid P to achieve a $1^{\circ}C$ rise per unit mass.
This property indicates that P is more resistant to temperature changes compared to Q when heated.
▶️ Answer/Explanation
Detailed solution:
Evaporation is a surface phenomenon where particles at the liquid’s surface gain enough kinetic energy to overcome intermolecular forces.
Water consists of covalent $H_{2}O$ units known as molecules, rather than isolated atoms or subatomic protons.
During this process, the most energetic individual molecules break free from the liquid phase and enter the gaseous state.
This results in a decrease in the average kinetic energy of the remaining liquid, often referred to as evaporative cooling.
Option D is incorrect because “tiny drops” would still be in the liquid phase and are much larger than individual particles.
Therefore, the correct answer is B, as evaporation involves the escape of individual molecules from the surface.
▶️ Answer/Explanation
Detailed solution:
Heating a gas increases the average kinetic energy ($E_k = \frac{1}{2}mv^2$) of its particles, causing them to move faster.
As particles move faster, they collide with the container walls more frequently and with greater change in momentum ($\Delta p$).
Since force is defined as $F = \frac{\Delta p}{\Delta t}$, the average force exerted by each collision on the walls increases.
Gas pressure is the total force per unit area ($P = \frac{F}{A}$) exerted by these particle collisions.
Consequently, the increased impact forces lead directly to a higher recorded gas pressure within the sealed volume.
Option A correctly identifies that the increase in force during wall strikes is the fundamental cause of the pressure rise.
▶️ Answer/Explanation
Detailed solution:
Thermal conduction is the process where thermal energy is transferred through a material. Copper is a metal and a very good thermal conductor, whereas wood is an insulator (a poor conductor). When one end is placed in ice at $0^{\circ}C$, the copper rod conducts thermal energy away from the student’s hand toward the ice much faster than the wooden rod does. Consequently, the end of the copper rod reaches a lower temperature more quickly. When touched, the copper rod feels colder because it removes energy from the finger at a higher rate, leading to the conclusion that Option A is correct.
▶️ Answer/Explanation
Detailed solution:
Surface color significantly affects the transfer of thermal energy via infrared radiation. Dull black surfaces are the best absorbers and best emitters of radiation, while shiny white surfaces are poor absorbers and poor emitters. Since object X is black and object Y is white, X will have a higher rate of absorption than Y. Additionally, for an object to remain at a constant temperature, the rate of emission must equal the rate of absorption. Because X absorbs more effectively than Y at the same temperature, it must also emit more effectively to maintain that equilibrium. Therefore, both the rate of absorption and the rate of emission for object X are higher than those for object Y.
▶️ Answer/Explanation
Detailed solution:
By definition, in a transverse wave, the direction of vibration of the particles (or the floating cork) is at right angles ($90^{\circ}$) to the direction of energy propagation.
The question states that the waves travel horizontally from $X$ to $Y$.
Since the wave travels horizontally, the medium must vibrate vertically to remain perpendicular to the motion.
Therefore, as the wave passes, the cork will move up and down about its equilibrium position.
While energy moves from $X$ to $Y$, the matter itself does not travel with the wave; it only oscillates.
Thus, the correct motion is represented by the vertical arrows in Option B.
▶️ Answer/Explanation
Detailed solution:
A magnifying glass uses a thin converging lens with the object placed at a distance $u$ such that $u < f$, where $f$ is the focal length.
In this configuration, the refracted rays diverge and never meet on the opposite side of the lens.
When extrapolated backwards, they form a magnified image on the same side as the object.
This image is virtual because it cannot be projected onto a screen and upright relative to the object.
Therefore, the image produced by a magnifying glass is always virtual, upright, and enlarged.
This corresponds to Option D.
▶️ Answer/Explanation
Detailed solution:
According to the law of reflection, the angle of incidence $i$ is equal to the angle of reflection $r$.
The incident ray hits the first mirror at an angle; drawing the reflected ray at an equal angle directs it toward the second mirror.
Upon hitting the second mirror, the ray reflects again such that $i = r$ relative to the second normal.
Because the mirrors are at $90^{\circ}$, the final reflected ray emerges parallel to the original incident ray but shifted upward.
Tracing this geometric path accurately shows the ray following a trajectory that aligns perfectly with point $B$ on the screen.
Therefore, the ray reaches the screen at the labelled position $B$.
▶️ Answer/Explanation
Detailed solution:
The refractive index $n$ is defined as the ratio of the speed of light in air (or vacuum), $v_{air}$, to the speed of light in the material, $v_{mat}$, expressed as $n = \frac{v_{air}}{v_{mat}}$.
The problem states that the speed in the material is $50\%$ of the speed in air, so $v_{mat} = 0.5 \times v_{air}$.
Substituting this into the formula gives $n = \frac{v_{air}}{0.5 \times v_{air}}$.
The velocity terms cancel out, leaving $n = \frac{1}{0.5}$, which calculates to $2.0$.
Refractive index is a dimensionless ratio, so it has no units, making option B the correct choice.
▶️ Answer/Explanation
Detailed solution:
White light is composed of different wavelengths, each corresponding to a specific color of the visible spectrum. When white light enters a medium like a glass prism, each wavelength travels at a different speed, causing them to refract by different amounts. This separation of white light into its constituent colors—Red, Orange, Yellow, Green, Blue, Indigo, and Violet—is specifically defined as dispersion. While refraction is the underlying cause of the bending, the term for the resulting “splitting” into a spectrum is dispersion. Therefore, Option B is the correct term for this process.
▶️ Answer/Explanation
Detailed solution:
Television broadcasting via satellite requires the satellite to remain at a fixed position relative to the Earth’s surface so that receiving dishes do not need to move. This is achieved using a geostationary orbit, where the orbital period is exactly $24$ hours. For the transmission of these signals, microwaves are used because they can penetrate the Earth’s atmosphere and reach satellites in space. Unlike infrared, which is easily absorbed by atmospheric moisture, microwaves provide the necessary range and bandwidth for high-speed data. Therefore, the combination of a geostationary satellite and microwave radiation is the standard for television re-transmission.
▶️ Answer/Explanation
Detailed solution:
Sound is a mechanical wave that travels faster in media with higher density and elasticity; therefore, the speed of sound in a solid like steel is significantly greater than in air ($v_{steel} > v_{air}$). When a wave passes from one medium to another, its frequency $f$ remains constant as it is determined by the source. According to the wave equation $v = f\lambda$, since frequency is constant, the wavelength $\lambda$ is directly proportional to the speed $v$. Because the speed increases when entering the steel, the wavelength must also increase ($\lambda_{steel} > \lambda_{air}$) to satisfy the relationship. Thus, both the speed and wavelength in steel are greater than in air.
▶️ Answer/Explanation
Detailed solution:
Magnetic field lines are defined to emerge from the North ($N$) pole and enter the South ($S$) pole.
In the diagram, the arrows point away from both $J$ and $K$, indicating that both are North ($N$) poles.
The relative strength of a magnetic field is indicated by the density or spacing of the field lines.
At point $X$, the field lines are much closer together compared to point $Y$, where there is a large gap between the diverging lines.
Therefore, the magnetic field is strongest at point $X$.
This identifies the correct sequence as $J = N$, $K = N$, and strongest field at $X$, which matches Row A.
▶️ Answer/Explanation
Detailed solution:
An electric field is defined as a region of space where an electric charge experiences a non-contact force.
By scientific convention, the direction of an electric field at any point is defined as the direction of the force exerted on a stationary positive test charge placed at that point.
The relationship between force $F$, charge $q$, and electric field $E$ is given by the equation $F = qE$.
Since the field direction follows the force on a positive charge, it points away from positive source charges and toward negative source charges.
Row A correctly identifies both the physical description of the field and its conventional direction.
Rows B, C, and D are incorrect as they either misstate the field’s effect or the charge type used for the direction convention.
▶️ Answer/Explanation
Detailed solution:
The resistance $R$ of a conductor is inversely proportional to its cross-sectional area $A$, expressed as $R \propto \frac{1}{A}$.
For a wire with a circular cross-section, the area is calculated using the formula $A = \pi r^{2}$ or $A = \frac{\pi d^{2}}{4}$.
Since $A$ is directly proportional to the square of the diameter ($A \propto d^{2}$), we can substitute this into the resistance relationship.
Substituting $d^{2}$ for $A$ gives $R \propto \frac{1}{d^{2}}$, meaning resistance is inversely proportional to the square of the diameter.
Therefore, as the diameter $d$ increases, the resistance $R$ decreases significantly by the square of that factor.
This confirms that option D is the mathematically correct relationship for the given physical properties.
▶️ Answer/Explanation
Detailed solution:
Initially, with $S$ open, only $R_2$ and $R_3$ are in series. Since $R_2 = R_3 = 20~\Omega$, the supply voltage $V_{total}$ splits equally: $V_{R2} = V_{R3} = 9.0~V$, so $V_{total} = 18~V$.
When $S$ is closed, $R_1$ and $R_2$ are in parallel. Their combined resistance is $R_{12} = \frac{20 \times 20}{20 + 20} = 10~\Omega$.
The circuit is now a series combination of $R_{12} = 10~\Omega$ and $R_3 = 20~\Omega$.
Using the potential divider formula, the new p.d. across $R_3$ is $V’_3 = V_{total} \times \left( \frac{R_3}{R_{12} + R_3} \right)$.
Substituting the values: $V’_3 = 18 \times \left( \frac{20}{10 + 20} \right) = 18 \times \frac{2}{3} = 12~V$.
▶️ Answer/Explanation
Detailed solution:
For an LED or diode to conduct, it must be forward-biased, meaning conventional current must flow in the direction of the triangle symbol ($+$ to $-$).
In these circuits, conventional current leaves the positive terminal ($+$) and attempts to return to the negative terminal ($-$).
In Circuit C, the current travels clockwise; it encounters the first LED, the center diode, and the second LED all pointing in the same clockwise direction.
Since all three components are forward-biased, the circuit is complete and both LEDs will illuminate.
In other options, at least one diode or LED is reverse-biased (pointing against the current), which blocks the flow for the entire series loop.
▶️ Answer/Explanation
Detailed solution:
To determine the direction of motion, we apply Fleming’s Right-Hand Rule for induced current.
The First Finger represents the magnetic field, pointing from North ($N$) to South ($S$) (rightward).
The Second Finger represents the direction of the induced current, which is pointing “out of the page” toward the observer as shown by the arrow on the wire.
The Thumb then points in the direction of the Motion (force) applied to the wire.
Aligning your hand accordingly, the thumb points vertically downward toward C.
Thus, to induce a current in the direction indicated, the wire must be moved in direction C.
▶️ Answer/Explanation
Detailed solution:
An a.c. generator converts mechanical energy into electrical energy using electromagnetic induction.
It requires a coil of wire (Option A) rotating between magnetic poles (Option C) to induce an e.m.f.
To maintain an alternating current output, it uses slip rings (Option D) to connect the rotating coil to the external circuit.
A split-ring commutator (Option B) is specifically used in d.c. motors to reverse current direction or in d.c. generators to rectify the output.
Therefore, the split-ring commutator is the component not found in an a.c. generator setup.
▶️ Answer/Explanation
Detailed solution:
The magnetic field around a straight current-carrying wire forms a circular pattern of concentric field lines.
To determine the direction, we use the Right-Hand Grip Rule: point the thumb in the direction of the current and the fingers curl in the direction of the magnetic field.
In the diagram, the current is flowing upwards toward the observer’s eye.
By pointing the thumb upward (out of the plane toward you), the fingers curl in an anticlockwise direction.
Therefore, the field is circular and moves anticlockwise, making Row A the correct description.
▶️ Answer/Explanation
Detailed solution:
A transformer works on the principle of electromagnetic induction, where an alternating current in the primary coil creates a changing magnetic field.
The iron core is a soft magnetic material that provides a high-permeability path for this magnetic flux.
Its primary purpose is to efficiently “link” or guide the magnetic field lines from the primary coil to the secondary coil.
This ensures that the maximum possible magnetic flux passes through the secondary coil to induce an electromotive force ($e.m.f.$).
It does not conduct electricity between the coils, as the primary and secondary circuits are electrically insulated from each other.
Therefore, option D correctly identifies the core’s role in magnetic linkage.
▶️ Answer/Explanation
Detailed solution:
In the Rutherford alpha-scattering experiment, a beam of α-particles is directed at a thin gold foil. Most α-particles pass straight through the foil with little or no deflection, as shown by direction A. This observation provides evidence that the atom consists of mostly empty space. Only a very small fraction of particles experience large deflections or reflect back, indicating a tiny, dense, positively charged nucleus. Since the majority of the atom’s volume is empty, most particles do not encounter the nucleus and continue their path undeflected. Therefore, direction A represents the path taken by the vast majority of the particles.
▶️ Answer/Explanation
Detailed solution:
The nucleon number (A), also known as the mass number, represents the total number of protons and neutrons in the nucleus.
The number of protons is given as 5, which is also the atomic number (Z).
The relationship between these quantities is given by the formula: A=Z+N, where N is the number of neutrons.
By rearranging the equation to solve for neutrons, we get N=A−Z.
Substituting the given values: N=11−5=6.
Therefore, there are 6 neutrons in this atom of boron, making option B the correct choice.
▶️ Answer/Explanation
Detailed solution:
First, find the initial corrected count rate by subtracting background: $800 – 32 = 768$ counts / minute.Since the half-life is $3$ hours, $6$ hours represents exactly two half-lives ($n = \frac{6}{3} = 2$).
After the first half-life, the rate becomes $\frac{768}{2} = 384$; after the second, it is $\frac{384}{2} = 192$ counts / minute.
The detector measures the source plus background, so add the background back: $192 + 32 = 224$ counts / minute.
This matches Option C, which accounts for both the decay of the isotope and the constant background radiation.
▶️ Answer/Explanation
Detailed solution:
In $\beta$-decay, a neutron in the nucleus changes into a proton and an electron, represented as $^{1}_{0}n \rightarrow\ ^{1}_{1}p +\ ^{0}_{-1}e$.
The nucleon number ($A$) remains constant because the total number of nucleons does not change ($24 \rightarrow 24$).
The proton number ($Z$) increases by $1$ as a new proton is formed ($11 \rightarrow 12$).
Conservation of charge requires the sum of bottom indices to be equal: $11 = 12 + (-1)$.
Conservation of mass requires the sum of top indices to be equal: $24 = 24 + 0$.
Therefore, $^{24}_{11}\text{Na}$ decays into $^{24}_{12}\text{Mg}$, making equation A the correct representation.
▶️ Answer/Explanation
Detailed solution:
Safety when handling radioactive sources depends on minimizing the total dose received by the body.
Reducing the time of exposure directly limits the quantity of radiation absorbed by tissues.
Using shielding, such as thick lead or concrete, absorbs the highly penetrating $\gamma$-rays before they reach the person.
Increasing distance is a primary safety rule because radiation intensity follows the inverse square law, $I \propto \frac{1}{d^{2}}$.
Statement 1 is incorrect because reducing the distance would significantly increase the radiation intensity and danger.
Therefore, only statements 2 and 3 are valid safety precautions, making D the correct choice.
▶️ Answer/Explanation
Detailed solution:
To solve this, we compare the approximate durations of each defined period:
1. T R (Earth’s rotation) is approximately 24 hours or 1 day.
2. T M (Moon’s orbit around Earth) is approximately 1 month (specifically ≈27.3 days).
3. T S (Earth’s orbit around the Sun) is approximately 365 days or 1 year.
Comparing these values: 24 hours < 1 month < 1 year.
Therefore, T R is the shortest period and T S is the longest period.
This corresponds exactly to the configuration shown in Row B.
▶️ Answer/Explanation
Detailed solution:
Redshift is defined as an increase in the observed wavelength of electromagnetic radiation from receding sources.
Observations show that light from distant galaxies is shifted toward the red end of the spectrum, making statement C correct.
Statement A is incorrect because there are billions of galaxies, while $100000$ light-years is the approximate diameter of the Milky Way.
Statement B is false because redshift involves an increase in wavelength, not a decrease.
Statement D is incorrect because redshift provides evidence that the Universe is expanding, supported by the Big Bang Theory.
Therefore, only statement C accurately reflects the observed astronomical phenomena described in the syllabus.
▶️ Answer/Explanation
Detailed solution:
CMBR was produced shortly after the Universe formed as high-energy radiation with short wavelengths.
As the Universe expanded, the space through which this radiation travelled also stretched, a process known as cosmological redshift.
This stretching increased the wavelength λ of the radiation over time, shifting it from the gamma or X-ray region into the microwave region.
Since the wavelength has been increasing, it follows that the CMBR had a much shorter wavelength in the past.
Consequently, the frequency f has decreased over time because v=fλ, making options A and B incorrect.
Option D is incorrect as CMBR was emitted relatively early in the history of the Universe.