▶️ Answer/Explanation
Detailed solution:
The volume of an irregular solid that sinks can be found by measuring the rise in water level when it is submerged in a measuring cylinder.
While the balance could give the mass, it cannot determine volume without additional density information.
Since the sphere is small and metal, it will sink, making the water displacement method in the measuring cylinder suitable.
No other apparatus is needed to calculate volume using this technique.
Thus, only the measuring cylinder containing water is required to find the volume of the sphere.
▶️ Answer/Explanation
Detailed solution:
The forces acting on the object are 4 N to the left and 3 N to the right.
Since the forces are in opposite directions, the resultant force is found by subtracting the smaller force from the larger force: 4 N − 3 N = 1 N.
The direction of the resultant force is the same as the direction of the larger force, which is to the left.
Therefore, the resultant force on the object is 1 N to the left.
▶️ Answer/Explanation
Detailed solution:
As the ball falls, its height decreases, so the energy stored in the gravitational potential store decreases.
Simultaneously, the speed of the ball increases, meaning the energy in the kinetic store increases.
This process represents a transfer of energy from the gravitational potential store to the kinetic store via mechanical working done by gravity.
There is no involvement of elastic (strain) energy since the ball is not being deformed.
Therefore, the only correct energy transfer pathway described is gravitational potential energy to kinetic energy.
Hence, option C is the correct answer.
▶️ Answer/Explanation
Detailed solution:
A scalar quantity has only magnitude, while a vector has both magnitude and direction.
Row A shows speed (scalar) and velocity (vector), fitting the requirement perfectly.
Rows B and D contain two vectors each (acceleration & force; velocity & acceleration).
Row C contains two scalars (speed and distance).
Thus, only Row A includes exactly one scalar and one vector quantity.
▶️ Answer/Explanation
Detailed solution:
Liquids with higher density sink below those with lower density when they do not mix.
From the table, densities in g/cm³ are: W = 1.2, X = 0.9, Y = 1.0, Z = 1.1.
Order from bottom to top (highest to lowest density): W (1.2), Z (1.1), Y (1.0), X (0.9).
Z (1.1 g/cm³) is denser than Y (1.0 g/cm³), so Z forms the layer below Y.
W forms the bottom layer, not below X; X forms the top layer; Y is not at the bottom.
Thus, only statement D is correct.
▶️ Answer/Explanation
Detailed solution:
For a balanced beam, the sum of clockwise moments equals the sum of anticlockwise moments about the pivot.
Force R creates an anticlockwise moment (R × a), while force Q creates a clockwise moment (Q × b).
Force P acts at a perpendicular distance d from the pivot, producing an anticlockwise moment (P × d).
Equating moments: (P × d) = (R × a) + (Q × b), which rearranges to (P × d) – (Q × b) = (R × a).
This matches option D, correctly applying the principle of moments with perpendicular distances.
▶️ Answer/Explanation
Detailed solution:
Change in momentum Δp = m(v – u) = 5.0 kg × (–4.0 m/s – 3.0 m/s).
This gives Δp = 5.0 × (–7.0) = –35 kg m/s.
The negative sign indicates the change is in the opposite direction to the initial velocity.
Momentum is a vector quantity, so direction must be considered when calculating change.
Thus, the magnitude and sign show a reversal and increase in speed, resulting in option A.
▶️ Answer/Explanation
Detailed solution:
Pressure due to a liquid column is given by \(p = \rho g h\). From the diagram, height \(h = 0.50 \mathrm{~m}\) and \(p = 6000 \mathrm{~Pa}\). Using \(g = 10 \mathrm{~m/s^2}\), \(\rho = \frac{p}{gh} = \frac{6000}{10 \times 0.5} = 1200 \mathrm{~kg/m^3}\). This matches the calculation for density using the given pressure and depth.
▶️ Answer/Explanation
Detailed solution:
Condensation is the specific term used for the change of state from a gas to a liquid.
Melting refers to a solid changing to a liquid, not a liquid to a solid (which is freezing).
Solids do not condense; they melt to become liquids, and boiling is a process specific to liquids turning into gases.
The only statement that accurately pairs the state change with the correct terminology is option A.
Therefore, option A is the correct description of a change of state.
▶️ Answer/Explanation
Detailed solution:
The base of a cooking pan must be a good thermal conductor, such as metal, to efficiently transfer heat to the food.
The handle must be a poor thermal conductor (a good insulator), such as wood or plastic, to prevent burning the user’s hand.
A metal handle would conduct heat quickly and become too hot to hold safely, making it unsuitable for the handle.
Therefore, the correct combination is a metal base for conductivity and a wood handle for insulation, which matches row B.
▶️ Answer/Explanation
Detailed solution:
To raise the water temperature at the quickest rate, the pipe surface must be a good absorber of infrared radiation.
Dull, black surfaces are the best absorbers (and emitters) of thermal radiation, while shiny, white surfaces are good reflectors.
A dull black coating maximizes the absorption of solar energy, transferring more heat to the water inside.
Shiny or white surfaces would reflect much of the incident radiation, reducing the heating effect.
Therefore, the combination of a dull texture and black colour ensures the most efficient thermal energy transfer.
Consequently, option A is the correct choice for this application.
▶️ Answer/Explanation
Detailed solution:
This continuous, random motion of visible particles (pollen grains) suspended in a fluid is known as Brownian motion.
It is caused by the invisible, fast-moving water molecules colliding with the much larger pollen grain.
At any instant, the number of molecules striking one side of the grain will be different from the other side, creating a resultant force.
This uneven bombardment on different sides causes the grain to move randomly in a zig-zag path.
A single molecular collision (Option B) would be insufficient to move the relatively massive grain significantly.
Therefore, the correct explanation is the uneven bombardment by water molecules.
▶️ Answer/Explanation
Detailed solution:
Evaporation rate increases with larger surface area and greater air movement, making suggestions 1 and 3 correct.
Cooling the water (suggestion 2) reduces the average kinetic energy of particles, decreasing the rate of evaporation.
Therefore, only pouring into a wider dish and using a fan will increase the rate at which water turns into vapor.
Option C correctly identifies these two factors based on the principles of the particle model.
▶️ Answer/Explanation
Detailed solution:
In a liquid, particles are arranged close together but not in a fixed pattern, allowing them to slide past one another.
The motion of particles in a liquid is described as random, with particles moving freely throughout the volume of the liquid.
This contrasts with solids (fixed pattern, vibrate) and gases (far apart, random and fast).
The separation in liquids is small enough to maintain a definite volume but not a definite shape.
Therefore, row B correctly identifies both the arrangement and motion of particles in a liquid.
▶️ Answer/Explanation
Detailed solution:
Using the formula \(\Delta \theta = \frac{\Delta E}{mc}\), substitute the values: \(\Delta E = 2250 \text{ J}\), \(m = 0.100 \text{ kg}\), \(c = 900 \text{ J/(kg °C)}\).
This gives \(\Delta \theta = \frac{2250}{0.100 \times 900} = \frac{2250}{90} = 25 \text{ °C}\).
The calculation shows the maximum temperature rise is exactly \(25 \text{ °C}\), assuming no heat losses.
Therefore, option C is correct.
▶️ Answer/Explanation
Detailed solution:
In a wave diagram, the amplitude is the maximum displacement from the rest position, shown by distance R from the peak to the equilibrium line.
The wavelength is the distance between two consecutive identical points on the wave, such as from peak to peak, represented by distance Q.
Distance P corresponds to the vertical height between a crest and a trough, which is twice the amplitude.
Distance S measures a partial horizontal displacement and does not represent the full wavelength of the wave.
Therefore, the correct identification of wave properties is R as amplitude and Q as wavelength.
▶️ Answer/Explanation
Detailed solution:
An image in a plane mirror is always virtual because the reflected rays appear to diverge from behind the mirror.
It is the same size as the object and is located at the same perpendicular distance behind the mirror as the object is in front.
The image is laterally inverted (left and right are reversed) but it is upright, not inverted.
Rows A and C are incorrect as they describe the image as real; row B is wrong because the image is not diminished.
Only row D correctly identifies the image as virtual, same size, and same distance from the mirror.
Therefore, option D accurately states the characteristics of a plane mirror image.
▶️ Answer/Explanation
Detailed solution:
The typical human audible range is 20 Hz to 20,000 Hz.
Elephants can hear sounds as low as 10 Hz, which is below the human lower limit of 20 Hz.
Horses can hear frequencies up to 33,000 Hz, exceeding the human upper limit of 20,000 Hz.
Therefore, humans cannot hear the lowest frequencies detected by elephants nor the highest frequencies detected by horses.
This means the human ear cannot hear all sounds heard by either animal.
Option D correctly states this limitation in both the low and high frequency ranges.
▶️ Answer/Explanation
Detailed solution:
The image formed by a plane mirror is always virtual, upright, and located the same distance behind the mirror as the object is in front.
In the diagram, the object is placed to the left of the mirror, so its image will appear directly opposite behind the mirror at an equal perpendicular distance.
Option A shows the image correctly positioned along the same horizontal line as the object, behind the mirror plane.
The other options place the image incorrectly either in front of the mirror or at a different relative location.
This follows the law of reflection and the principle that the image is formed where the reflected rays appear to diverge from behind the mirror.
▶️ Answer/Explanation
Detailed solution:
The refractive index \(n\) is defined as \(n = \frac{\sin i}{\sin r}\), where \(i\) is the angle in air and \(r\) is the angle in glass. In the diagram, the angles are measured from the *boundary*, not the normal. The angle of incidence \(i = 90^\circ – \Theta_1\) and the angle of refraction \(r = 90^\circ – \Theta_2\). Therefore, \(n = \frac{\sin(90^\circ – \Theta_1)}{\sin(90^\circ – \Theta_2)}\). This matches option C when simplified, as the angle in the glass (\(\Theta_2\)) is measured from the normal in the diagram. Option A uses the angles from the boundary directly, which is incorrect. Option B mixes the boundary angle for incidence with the normal angle for refraction. Thus, C is the correct expression for the refractive index.
▶️ Answer/Explanation
Detailed solution:
From the diagram, angle of incidence \(i = 56^\circ\) and angle of refraction \(r = 33^\circ\). Using Snell’s law, \(n = \frac{\sin i}{\sin r} = \frac{\sin 56^\circ}{\sin 33^\circ} \approx 1.5\).
Refractive index \(n = \frac{\text{speed in air}}{\text{speed in glass}}\), so speed in glass = \(\frac{3.0 \times 10^8}{1.5} = 2.0 \times 10^8 \, \text{m/s}\).
This matches option B; the other options do not correspond to the correct calculation using the given angles.
Thus, the speed of light in the glass is \(2.0 \times 10^8 \, \text{m/s}\).
▶️ Answer/Explanation
Detailed solution:
A converging (convex) lens is thicker at the centre and brings parallel light rays to a focus at the principal focus.
A diverging (concave) lens is thinner at the centre and causes parallel light rays to spread out.
A converging lens can form a real image, for example when an object is placed beyond the focal length.
A diverging lens cannot form a real image on a screen; it always produces a virtual image.
Therefore, the row stating converging lenses can form real images and diverging lenses cannot is correct.
▶️ Answer/Explanation
Detailed solution:
The balance reading decreases, indicating an upward force on rod X reducing its apparent weight.
This occurs when there is an attractive force pulling X upward toward Y.
According to electrostatic principles, opposite charges (positive and negative) attract each other.
If both rods had the same charge (both positive or both negative), they would repel, increasing the reading.
Therefore, the correct combination must be one rod charged positive and the other charged negative.
Thus, option A correctly identifies the charge combination causing the observed decrease in the balance reading.
▶️ Answer/Explanation
Detailed solution:
Potential difference is defined as the work done per unit charge and is measured using a voltmeter.
The unit volt (V) is equivalent to one joule per coulomb (\(1\,V = 1\,J/C\)).
The ampere is the unit of electric current, while the coulomb measures electric charge.
Coulomb per second is the definition of an ampere, not the unit of potential difference.
Therefore, option D correctly identifies the volt as the SI unit for potential difference.
▶️ Answer/Explanation
Detailed solution:
Using the transformer equation Vp/Vs = Np/Ns, we substitute the given values: 230 V / Vs = 500 turns / 10000 turns.
This simplifies to 230 / Vs = 1/20, so Vs = 230 × 20 = 4600 V.
The transformer has more secondary turns than primary turns, making it a step-up transformer that increases voltage.
Options A and B are too low, while option D is far too high for this turns ratio.
Therefore, the correct output voltage is 4600 V, corresponding to option C.
▶️ Answer/Explanation
Detailed solution:
Magnetic field strength is indicated by the spacing of field lines: closer lines mean a stronger field.
At point R, the opposite poles (N and S) face each other, creating a concentrated, uniform field with closely packed lines—hence the strongest field.
At point Q, the field lines from the two north poles repel and spread out into the surrounding space, resulting in a much weaker field.
Point P lies near a single pole where field lines are moderately dense, giving an intermediate strength.
Thus, the weakest field is at Q and the strongest is at R, making option B the correct choice.
▶️ Answer/Explanation
Detailed solution:
Resistance \( R \) is proportional to length \( L \) and inversely proportional to cross-sectional area \( A \) (\( R \propto \frac{L}{A} \)).
Wire Q has double the length of P, which would double the resistance.
However, diameter is doubled, making the area (\( \propto d^2 \)) four times larger, reducing resistance by a factor of four.
Combining these changes: \( R_Q = R_P \times \frac{2}{4} = \frac{1}{2} R_P \).
Therefore, the resistance of Q is exactly one-half the resistance of wire P.
Option B is the correct comparison based on the proportional relationships.
▶️ Answer/Explanation
Detailed solution:
When resistors are connected in parallel, the total resistance is always less than the smallest individual resistance.
Here, the \(40 \text{ k}\Omega\) resistor is extremely large compared to the \(2.0 \Omega\) resistor, so it conducts negligible current.
The combined parallel resistance is effectively just slightly less than \(2.0 \Omega\), and for practical purposes rounds to \(2.0 \Omega\).
In series, the resistances add directly: \(2.0 \Omega + 40000 \Omega = 40002 \Omega\), not \(42 \Omega\).
Therefore, the only correct statement is that the parallel combination gives approximately \(2.0 \Omega\).
▶️ Answer/Explanation
Detailed solution:
In circuit C, both lamps are connected in parallel with the battery, so each receives the full source voltage and lights up.
In circuit A, the diode is reverse-biased, preventing any current flow, so neither lamp lights.
In circuit B, the diode is forward-biased, but one lamp is short-circuited by a wire, so current bypasses it and only one lamp lights.
In circuit D, the lamps are in series but the switch is open, breaking the circuit and preventing current flow.
Therefore, only circuit C provides a complete path for current through both lamps.
▶️ Answer/Explanation
Detailed solution:
In nuclide notation \(_{Z}^{A}\textrm{X}\), Z is the proton number and A is the nucleon number.
Here, Z = 38, so the nucleus contains 38 protons.
The number of neutrons is found using A – Z = 84 – 38 = 46 neutrons.
This matches the values in option A: 38 protons and 46 neutrons.
The other options incorrectly swap or miscalculate the proton and neutron counts.
▶️ Answer/Explanation
Detailed solution:
Background radiation is always present and contributes to the total count rate measured by a detector.
To find the true count rate from the radioactive substance alone, the background count must be deducted.
This is done by measuring the background rate without the source and subtracting it from the reading with the source.
Options A and B would give an inflated or inaccurate result, while D reduces random error but does not eliminate background.
Therefore, the correct adjustment is to subtract the background count from the reading.
▶️ Answer/Explanation
Detailed solution:
Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus.
This process releases a significant amount of energy, which powers stars like the Sun.
Option B is incorrect because energy is emitted, not absorbed, during fusion.
Options C and D describe nuclear fission, which involves the splitting of a heavy nucleus.
Therefore, the correct description of nuclear fusion is two light nuclei joining with the emission of energy.
▶️ Answer/Explanation
Detailed solution:
An electron (beta-particle) is negatively charged, so it experiences an electric force opposite to the direction of the electric field.
To deflect the electron downwards, the electric force must act downwards, requiring the electric field to point upwards.
This is because \( \vec{F} = q\vec{E} \), and with \( q \) negative, \( \vec{F} \) and \( \vec{E} \) are in opposite directions.
Options A and B describe fields perpendicular to the required deflection plane and would not cause downward motion.
Option C would produce an upward force on a negative charge, deflecting it upwards instead of downwards.
Thus, an upward electric field (Option D) is needed to deflect an electron downwards.
▶️ Answer/Explanation
Detailed solution:
Alpha decay reduces the nucleon number (mass number) by 4 and the proton number (atomic number) by 2.
Starting with radon \( _{86}^{222}\textrm{Rn} \), the daughter polonium nucleus will have \( A = 222 – 4 = 218 \) and \( Z = 86 – 2 = 84 \).
The number of neutrons is calculated as nucleon number minus proton number: \( N = A – Z = 218 – 84 = 134 \).
Therefore, the polonium isotope produced contains 134 neutrons in its nucleus.
Option C is the correct answer.
▶️ Answer/Explanation
Detailed solution:
To minimise the harmful effects of ionising radiation, exposure time should be reduced and distance from the source increased.
Decreasing time limits the total dose received, while increasing distance reduces intensity due to the inverse square law.
Options A, C, and D suggest unsafe practices that would increase radiation exposure and potential biological damage.
Shielding is the third key precaution, but this question specifically addresses time and distance.
Therefore, option B correctly identifies the two essential safety measures when handling radioactive materials.
▶️ Answer/Explanation
Detailed solution:
The order of planets from the Sun outward is Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
The question asks for decreasing order of distance, meaning from farthest to nearest to the Sun.
Neptune is the farthest planet, followed by Uranus, then Saturn, and finally Jupiter among the outer planets.
Option C correctly lists Neptune → Uranus → Saturn → Jupiter, matching the required decreasing distance order.
Options A, B, and D either reverse the order or incorrectly place Uranus and Neptune relative to each other.
Thus, C is the correct sequence.
▶️ Answer/Explanation
Detailed solution:
The Sun emits energy across the entire electromagnetic spectrum, but most of its output is concentrated in three main regions.
According to the syllabus, the Sun radiates most of its energy in the infrared, visible light, and ultraviolet regions.
Given that region 1 is infrared and region 2 is visible light, the remaining region 3 must correspond to ultraviolet radiation.
Microwaves and radio waves have longer wavelengths and lower energy, while X-rays have shorter wavelengths and higher energy than ultraviolet.
Therefore, based on the typical distribution of solar radiation, region 3 is ultraviolet.
▶️ Answer/Explanation
Detailed solution:
According to the conservation of energy, a comet in an elliptical orbit moves fastest when it is closest to the Sun (perihelion).
At this position, gravitational potential energy is at a minimum, so kinetic energy and speed are maximized.
In the diagram, position A is nearest to the Sun, meaning the comet’s orbital speed is greatest there.
As the comet moves away from the Sun, it slows down due to the increasing gravitational potential energy.
Therefore, the greatest speed occurs at position A.
▶️ Answer/Explanation
Detailed solution:
The Sun’s energy is produced by nuclear fusion, where lighter nuclei combine to form heavier ones.
In the Sun’s core, hydrogen nuclei (protons) fuse together under extreme temperature and pressure to form helium.
This process releases vast amounts of energy in the form of electromagnetic radiation.
Fission, the splitting of heavy nuclei, is not the process powering the Sun.
Therefore, the correct description is the fusion of hydrogen into helium.
▶️ Answer/Explanation
Detailed solution:
Planet X has a low density, large diameter, and is far from the Sun, matching the characteristics of Jupiter.
Planet Y has a high density, small diameter, and orbits very close to the Sun, matching the characteristics of Mercury.
Jupiter is the largest gas giant, while Mercury is the smallest rocky planet nearest to the Sun.
The combination of distance, density, and diameter confirms X as Jupiter and Y as Mercury.
Thus, option A correctly identifies both planets based on the given data.