▶️ Answer/Explanation
Detailed solution:
From the diagram, the total length of six identical balls placed in a row is measured to be $24\text{ cm}$.
Since the balls are identical, the diameter of one ball is found by dividing the total length by the number of balls.
Calculation: Diameter $= \frac{24\text{ cm}}{6} = 4\text{ cm}$.
This method of measuring multiples reduces the uncertainty in finding the small distance of a single diameter.
Therefore, the diameter of one ball is $4\text{ cm}$, matching Option A.
▶️ Answer/Explanation
Detailed solution:
The graph shows $y$ remains constant over time. If $y$ is distance and the train is stationary (1), distance doesn’t change, matching the graph.
If $y$ is speed and the train moves at constant speed (4), the speed graph would be a horizontal line.
Statement (2) is false as moving changes distance; statement (3) is false as stationary means zero speed.
Thus, only statements 1 and 4 can be true, corresponding to Option B.
▶️ Answer/Explanation
Detailed solution:
Weight is calculated using the equation \(W = mg\), where \(m\) is mass and \(g\) is the gravitational field strength.
Substitute the given values: \(W = 200 \text{ kg} \times 3.7 \text{ m/s}^2\).
This gives \(W = 740 \text{ N}\).
The weight depends on the local gravitational field strength, not Earth’s value of \(9.8 \text{ N/kg}\).
Therefore, the correct answer is Option C.
▶️ Answer/Explanation
Detailed solution:
Mass is the quantity of matter in an object and does not change with location.
Weight is the gravitational force on an object and depends on the gravitational field strength.
On the Moon, gravity is weaker, so weight decreases, but the mass remains constant.
Option A is wrong as floating objects still have weight; Option B confuses the two concepts.
Option C is incorrect because mass is measured in kilograms, while newtons measure weight.
▶️ Answer/Explanation
Detailed solution:
Density is calculated using the equation \(\rho = \frac{m}{V}\), where \(m\) is the mass of the object alone and \(V\) is the volume of the object alone.
The balance reading of \(78.0\text{ g}\) represents the mass \(m\) of the solid.
The volume \(V\) of the solid is found by the displacement method: Final volume (\(69.5\text{ cm}^3\)) – Initial volume (\(60.0\text{ cm}^3\)) = \(9.5\text{ cm}^3\).
Therefore, the correct values to use are the mass of the solid and the volume difference (the volume of the solid itself).
This corresponds to Option A.
▶️ Answer/Explanation
Detailed solution:
For the rod to be in equilibrium, there must be no resultant force and no resultant moment.
The pivot is at the centre, so the perpendicular distances from the pivot to the lines of action of the forces must be considered.
In option A, the two equal forces are applied at equal distances on opposite sides of the pivot, creating equal and opposite moments.
Thus, the clockwise moment cancels the anticlockwise moment, resulting in no resultant moment and equilibrium.
Options B, C, and D show unbalanced forces or unequal moments, causing the rod to rotate.
▶️ Answer/Explanation
Detailed solution:
The moment of a force about a pivot is defined as the product of the force and the perpendicular distance from the pivot to the line of action of the force.
From the diagram, force Y acts vertically downward, and its line of action is a perpendicular distance $b$ from the pivot.
Therefore, the moment of force Y is correctly calculated as $Y \times b$.
Option A is incorrect because $a + b$ is not the perpendicular distance for force Y; it is the total length of the beam.
Options B and D are incorrect as they involve division rather than multiplication.
▶️ Answer/Explanation
Detailed solution:
Gravitational potential energy depends on height, so the least is at the lowest point (Point C).
Elastic potential energy in the spring depends on extension or compression, so the most is at maximum stretch (Point A).
Therefore, the correct combination is least gravitational at C and most elastic at A.
This matches Option D in the table provided.
▶️ Answer/Explanation
Detailed solution:
Renewable resources are those that are naturally replenished on a human timescale. From the list, biofuels, tidal, geothermal, hydroelectric, and solar (light from the Sun) are renewable.
Fossil fuels and nuclear fuel are non-renewable as they exist in finite deposits.
Counting the renewable items gives a total of $5$.
This corresponds to Option C.
▶️ Answer/Explanation
Detailed solution:
Power is defined as the rate of energy transfer, measured in watts (W).
One watt is equivalent to one joule per second ($1\text{ W} = 1\text{ J/s}$).
Therefore, a rating of $900\text{ W}$ means the microwave transfers $900\text{ joules}$ of electrical energy into heat and other forms every second.
Options B, C, and D are incorrect as they confuse the units for current, potential difference, and resistance.
▶️ Answer/Explanation
Detailed solution:
Pressure is defined as force per unit area (\(p = \frac{F}{A}\)).
A sharp nail has a much smaller surface area at its point compared to a blunt nail.
When the same pushing force is applied, the smaller area of the sharp nail results in a significantly larger pressure on the wood.
This higher pressure makes it easier for the nail to penetrate the surface.
Therefore, the sharp nail exerts a larger pressure, making Option C correct.
▶️ Answer/Explanation
Detailed solution:
Heating the air increases the kinetic energy of the particles, so their average speed increases.
Since the bottle is sealed and has a constant volume, the particles cannot expand or move further apart; the average distance between them remains unchanged.
Therefore, the average speed increases while the average distance stays the same.
This corresponds directly to the option where speed increases and distance stays the same.
▶️ Answer/Explanation
Detailed solution:
According to Boyle’s law, for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: $p \propto \frac{1}{V}$.
This relationship produces a hyperbolic curve on a $p$–$V$ graph, where pressure decreases as volume increases.
Option C correctly shows this inverse proportionality with a smooth curve approaching but never touching the axes.
Option A shows a linear decrease, B shows no relationship, and D shows direct proportionality, all of which are incorrect.
Therefore, the graph in Option C accurately represents the $pV = \text{constant}$ relationship.
▶️ Answer/Explanation
Detailed solution:
When a solid such as a metal block is heated, the particles vibrate more and move slightly further apart.
This increased separation occurs in all directions throughout the material.
Consequently, the expansion is not limited to a single dimension; it results in an increase in width, height, and length simultaneously.
This uniform expansion in all linear dimensions is a key characteristic of the thermal expansion of solids.
▶️ Answer/Explanation
Detailed solution:
During melting, the energy supplied (input of energy) is used to break the intermolecular bonds between particles rather than increasing their kinetic energy.
As a result, the temperature of the substance remains constant at its melting point until all of the solid has changed into a liquid.
Options A, B, and D are incorrect because they either suggest a temperature increase or no energy input, which contradicts the process of a phase change.
This matches Option C.
▶️ Answer/Explanation
Detailed solution:
Air near the heater is warmed, expands, and becomes less dense, rising upwards.
Cooler, denser air moves in to replace it, creating a convection current.
Therefore, the air moving through the gap under the cupboard is the cooler air flowing towards the heater.
This matches the description of cool air moving towards the heater in Row B.
▶️ Answer/Explanation
Detailed solution:
Waves are disturbances that propagate through a medium or space, transferring energy from one point to another.
Importantly, the particles of the medium (if present) oscillate about a fixed position and are not transported with the wave.
Options A, B, and C are incorrect: mechanical waves require a medium, wave speeds vary, and S-waves are transverse.
Therefore, the fundamental principle that waves transfer energy without transferring matter is the correct statement.
▶️ Answer/Explanation
Detailed solution:
The amplitude is the maximum displacement from the undisturbed position, measured vertically from the center line to a crest or trough.
The wavelength is the horizontal distance between two consecutive corresponding points on the wave, such as crest to crest or trough to trough.
In the diagram, distance Y represents the amplitude and distance Z represents one complete wavelength.
Therefore, the row identifying amplitude as Y and wavelength as Z is correct.
This matches Option B.
▶️ Answer/Explanation
Detailed solution:
When white light undergoes dispersion through a glass prism, violet light is refracted the most and red light the least.
Therefore, the spectrum on the wall will have red at the top (Y) and violet at the bottom (X), with green in the middle (Z).
Option C correctly assigns red to Y, green to Z, and violet to X.
This aligns with the known order of increasing frequency and decreasing wavelength from red to violet.
▶️ Answer/Explanation
Detailed solution:
The angle of incidence is measured between the incident ray and the normal (a line perpendicular to the mirror).
Since the ray makes an angle of $35^{\circ}$ with the mirror surface, the angle of incidence is $90^{\circ} – 35^{\circ} = 55^{\circ}$.
According to the law of reflection, the angle of reflection is equal to the angle of incidence.
Therefore, the angle of reflection is also $55^{\circ}$.
This corresponds to Option B.
▶️ Answer/Explanation
Detailed solution:
A real image formed by a converging lens is always inverted (upside down) relative to the object.
Since the top of the object (arrow) is above the principal axis, its image must be formed below the principal axis on the photo-sensitive surface.
In the diagram, only position C lies on the surface and is inverted relative to the object’s top.
Therefore, the correct position for the image of the top of the object is C.
▶️ Answer/Explanation
Detailed solution:
The spectrum diagram shows decreasing wavelength and increasing frequency from left to right.
Between ultraviolet and X-rays is the narrow visible light region, making E = visible light.
To the right of X-rays are gamma rays, which have the highest frequency and shortest wavelength, making G = gamma rays.
Therefore, the correct sequence for E, F, and G is visible light, X-rays, gamma rays, which corresponds to Option D.
▶️ Answer/Explanation
Detailed solution:
The speed of sound depends only on the medium (air), so it remains the same for the echo.
The frequency of a wave is determined by the source and does not change upon reflection.
Since wave speed $v = f\lambda$ and both $v$ and $f$ are unchanged, the wavelength $\lambda$ also remains unchanged.
Therefore, the echo has the same speed, frequency, and wavelength as the original sound.
This corresponds to the properties listed in Option B.
▶️ Answer/Explanation
Detailed solution:
Magnetic materials are those that experience a force when placed in a magnetic field.
Common magnetic metals include iron, nickel, cobalt, and alloys like steel.
Zinc, lead, and copper are non-magnetic materials and are not attracted to a magnet.
Iron is a ferromagnetic material and is strongly attracted by a magnet.
Therefore, the only correct choice is iron (Option C).
▶️ Answer/Explanation
Detailed solution:
An ammeter must be connected in series with the component to measure the current flowing through it.
In circuit 1, the ammeter is in series with the resistor, so it measures the correct current.
In circuit 2, the ammeter is also in series with the resistor, correctly measuring the current.
In circuit 3, the ammeter is connected in parallel with the resistor, which would create a short circuit and not measure the current through the resistor correctly.
Therefore, only circuits 1 and 2 have the ammeter connected correctly.
▶️ Answer/Explanation
Detailed solution:
Electrical conduction in metals occurs due to the presence of free (delocalised) electrons that move through the lattice.
Silver and gold are both excellent metallic conductors and contain a high density of free electrons.
Glass, water, and nylon are insulators or poor conductors with very few free electrons.
Copper is a good conductor, but it is paired with insulators in options B and C.
Only option D lists two metals, both of which have large concentrations of free electrons.
▶️ Answer/Explanation
Detailed solution:
Resistance is defined as the ratio of potential difference ($V$) to current ($I$), expressed as $R = \frac{V}{I}$.
The SI unit of potential difference is the volt ($V$) and current is the ampere ($A$).
Therefore, one unit of resistance is equivalent to one volt per ampere, which is defined as the ohm ($\Omega$).
This confirms Option B as the correct unit.
▶️ Answer/Explanation
Detailed solution:
To produce electrostatic charges by friction, the rod must be an electrical insulator so that charge does not flow away.
Glass and plastic are insulators, so they become charged when rubbed and retain the charge.
Copper and steel are electrical conductors, so any charge produced flows through the rod and the person’s hand to earth.
Therefore, only the glass rod and the plastic rod are suitable for this demonstration.
▶️ Answer/Explanation
Detailed solution:
For circuit 1 (series), total resistance is the sum: $R = 2.0\,\Omega + 3.0\,\Omega = 5.0\,\Omega$.
For circuit 2 (parallel), use the formula $\frac{1}{R} = \frac{1}{2.0} + \frac{1}{3.0} = \frac{5}{6}$, so $R = \frac{6}{5} = 1.2\,\Omega$.
Therefore, the total resistances are $5.0\,\Omega$ and $1.2\,\Omega$, which corresponds to row C in the table.
This matches the expected behaviour of series and parallel resistor combinations.
▶️ Answer/Explanation
Detailed solution:
The fuse rating must be slightly higher than the normal operating current of $5.0\text{ A}$ to prevent unnecessary blowing.
It must also be lower than the cable’s maximum current rating of $15\text{ A}$ to protect the cable from overheating.
The $10\text{ A}$ fuse satisfies both conditions: it is $> 5.0\text{ A}$ and $< 15\text{ A}$.
A $4.0\text{ A}$ fuse would blow during normal use, while $20\text{ A}$ or $40\text{ A}$ fuses would not protect the cable.
Therefore, the $10\text{ A}$ fuse is the most suitable choice.
▶️ Answer/Explanation
Detailed solution:
The magnitude of an induced e.m.f. depends on the rate of change of the magnetic field linking the coil.
Increasing the number of turns in the coil increases the total length of wire cutting the magnetic field lines.
This produces a larger induced e.m.f. for the same magnetic field and speed of movement.
Placing magnets further apart weakens the field, steel wire is less conductive, and reversing a magnet does not increase magnitude.
Therefore, increasing the number of turns is the correct method to increase the induced e.m.f.
▶️ Answer/Explanation
Detailed solution:
The direction of the force is determined by Fleming’s left-hand rule and is perpendicular to both the current and the magnetic field.
Reversing the current direction reverses the force direction, whereas changing the magnitude of current or field strength only affects the size of the force.
Using an electromagnet with the same polarity does not alter the field direction, so the force direction remains unchanged.
Therefore, reversing the current is the only change that will reverse the direction of the force.
▶️ Answer/Explanation
Detailed solution:
A transformer operates on the principle of electromagnetic induction and only functions with alternating current (a.c.).
Its primary purpose is to change (step up or step down) the magnitude of an alternating voltage.
It cannot change direct current into alternating current, alter the frequency, or act as a safety switch (which is the role of a fuse or circuit breaker).
Therefore, the only correct description of its use is changing the magnitude of an alternating voltage.
▶️ Answer/Explanation
Detailed solution:
A proton carries a positive charge (+1), a neutron has no charge (0), and an electron carries a negative charge (–1).
This matches the values listed in row C of the table.
These relative charges are fundamental to the nuclear model of the atom described in the syllabus.
Therefore, Option C is the correct choice.
▶️ Answer/Explanation
Detailed solution:
Time elapsed is $11400$ years, which equals $2$ half-lives ($11400 \div 5700 = 2$).
After one half-life, the count rate halves to $50$ counts/min; after two half-lives, it halves again to $25$ counts/min.
On the graph, the point corresponding to a count rate of $25$ counts/min at the appropriate time is point D.
This matches the expected decay after $11400$ years, confirming point D as the correct choice.
▶️ Answer/Explanation
Detailed solution:
Both alpha and beta decay involve a change in the number of protons in the nucleus, resulting in a different atomic number and thus a different element.
Gamma decay releases energy without changing the proton or nucleon number, so the element remains the same.
Therefore, both alpha-emission and beta-emission cause the nucleus to change into another element.
This corresponds to the image selection for Option A.
▶️ Answer/Explanation
Detailed solution:
Radioactive decay is a spontaneous nuclear process and is not affected by physical conditions such as temperature.
Therefore, cooling the source does not change its activity or the emission of γ-rays, providing no reduction in exposure.
Increasing distance, reducing exposure time, and using lead shielding are all established methods to minimize received radiation.
Consequently, keeping the temperature low is the action that will not reduce the total radiation reaching the scientist.
▶️ Answer/Explanation
Detailed solution:
The Earth rotates on its own tilted axis once every 24 hours, causing the daily cycle of day and night.
Option B (orbiting the Sun) takes approximately 365 days, which defines a year.
Option C (the Moon orbiting Earth) takes about one month, leading to the Moon’s phases.
Option D is incorrect as the Sun does not orbit the Earth; this is an outdated model.
▶️ Answer/Explanation
Detailed solution:
Statement 1 is correct: one light-year is the distance light travels in one year, so light from a star four light-years away takes four years to reach Earth.
Statement 2 is incorrect: the distance is four light-years one way, so a round trip for light would take eight years, not four.
Statement 3 is incorrect: the nearest star to the Sun (Proxima Centauri) is part of the Milky Way galaxy, so it is not outside our galaxy.
Therefore, only statement 1 is correct, making Option C the right choice.
▶️ Answer/Explanation
Detailed solution:
The Sun is composed mostly of hydrogen (and helium) as stated in the syllabus.
It radiates energy across the entire electromagnetic spectrum, but the peak intensity is in the visible light region.
Row D correctly identifies hydrogen as a primary constituent and visible light as a main radiation region.
Infrared and ultraviolet are also emitted, but visible light is the most prominent region specified.
Therefore, the correct match is Hydrogen and Visible light.