JAMB Physics 2018
Questions & Answers

Students might mistakenly select option D or B due to miscalculating the angle or the hypotenuse length when combining the directional components. Displacement is the straight-line distance from the starting point to the final position. A right-angled triangle with two equal legs of 1 km each is formed when the man walks 1 km east and then 1 km north. The hypotenuse calculated using the Pythagorean theorem gives √(1² + 1²) = √2 km. Finding the direction using trigonometry via tan(θ) = opposite/adjacent = 1/1 yields θ = 45°. Thus, the displacement is √2 km at 45° north of east, or N 45° E, which matches option A. Common mistake: incorrectly adding scalar distances instead of vector components to find the resultant displacement.

Students might mistakenly calculate 360 cm³ by confusing density division with multiplication, or pick 240 cm³ by multiplying the final density by the initial volume. The mass remains constant before and after frying since there is no loss of oil. Mass = volume × density = 400 cm³ × 0.9 g/cm³ = 360 g gives the initial mass. Volume = mass / density = 360 g / 0.6 g/cm³ = 600 cm³ is used to find the new volume after the density becomes 0.6 g/cm² following frying. An increase in volume occurred due to the decrease in density, likely caused by chemical changes or thermal expansion during frying, making 600 cm³ the correct new volume. Common mistake: failing to keep mass constant when calculating the new volume from a changed density.

Students might mistakenly pick only option A, B, or C because each individually describes a true electrical phenomenon, missing that all three statements are correct. All statements about electrical charge are correct. A deficit of electrons means a positive charge since removing negative electrons leaves a net positive charge as seen in ion structures, while an excess of electrons results in a negative charge. Electric current is defined as the flow of electric charge, typically the movement of electrons in conductors like metals. Since all these statements are accurate, the correct answer is 'All of the above.' Common mistake: stopping at the first recognized correct statement instead of evaluating all options.

Students might mistakenly select option B or D because they include X-rays, but X-rays are produced by atomic electron transitions or high-speed electron collisions rather than natural radioactive decay of nuclei. Natural radioactivity consists of the emission of α-particles, β-rays, and γ-rays. A more stable configuration is sought by unstable atomic nuclei through the spontaneous decay resulting in alpha particles as helium nuclei, beta particles as electrons or positrons, and gamma rays as high-energy electromagnetic radiation. Uranium-238 decays by emitting alpha particles, followed by beta and gamma emissions in its decay chain. Thus, natural radioactivity encompasses all three types of radiation, making option C correct. Common mistake: grouping artificially produced X-rays together with natural radioactive nuclear emissions.

Students might mistakenly choose 'Erect' or 'Laterally inverted' because they correctly describe mirror properties, failing to realize those are actual traits of plane mirror images. The image is not magnified; it has the same size as the object, with a magnification of 1, which means 'Magnified' does not describe the image formed by a plane mirror. Specific characteristics formed by a plane mirror include being erect or upright, laterally inverted with left and right reversed, and located at the same distance behind the mirror as the object is in front. Your image appears 2 meters behind it, upright, reversed, and the same size, but never enlarged if you stand 2 meters from a plane mirror, making 'magnified' the incorrect description. Common mistake: confusing the equal size of a plane mirror image with magnification.

Students might mistakenly choose 'Fission reaction' because both terms involve nuclear energy and splitting or combining atoms, but fission breaks heavy nuclei apart rather than merging light ones. This is characteristic of a nuclear fusion reaction, where light nuclei merge to form a heavier one, releasing energy due to the conversion of mass into energy (E=mc²). Two lighter nuclei X and Y each with mass number 2 and atomic number 1 combine to form a heavier nucleus Z with mass number 3 and atomic number 2, releasing a neutron (¹₀n) and energy in the given reaction. Hydrogen nuclei fuse to form helium in stars, releasing vast energy, matching the process described. Common mistake: confusing nuclear fusion of light elements with nuclear fission of heavy elements.

Students might mistakenly select option C or D because they involve kinetic, electrical, and heat energies, but the sequence must follow the actual operational flow from fuel burning to final lighting. Heat energy from burning fuel is converted into kinetic energy as steam moves pistons in a steam engine. Electromagnetic induction converts this kinetic energy into electrical energy by driving a generator. Light as a visible output and heat due to inefficiencies are transformed from this electrical energy when it powers a lamp. Coal heats water to produce steam in a power plant, which drives turbines to generate electricity that lights a bulb, producing both light and some heat, accurately described by option B. Common mistake: reversing the chronological energy conversion stages from thermal to mechanical to electrical.

Students might mistakenly pick 'High-energy electromagnetic waves' or 'Protons' because cathode rays involve radiation or subatomic particles, but they consist specifically of lightweight negative charges. Cathode rays are streams of electrons emitted from the cathode as a negative electrode in a vacuum tube when an electric current is passed through it. Electric and magnetic fields can deflect these rays, which travel in straight lines and carry a negative charge, as discovered in experiments by scientists like J.J. Thomson. Electrons from the cathode strike a phosphorescent screen to produce images in old cathode ray tube televisions, confirming that cathode rays are streams of electrons. Common mistake: confusing streams of electrons with electromagnetic waves like X-rays or gamma rays.

Students might mistakenly choose option B because they assume the prism contains the colors beforehand, but the prism merely acts as a dispersing medium rather than a reservoir of pre-existing colors. Different colours of white light travel with different speeds in glass, which is the correct explanation for why a narrow beam of white light can be split into different colours by a glass prism. Dispersion causes white light to pass through a glass prism and split into a spectrum of colors because white light comprises all visible wavelengths, with each color traveling at a different speed due to varying refractive indices. Red light travels faster and bends less with a longer wavelength, while violet light travels slower and bends more with a shorter wavelength, causing the colors to separate like a rainbow. Common mistake: assuming the glass prism itself colors the light rather than differentially refracting existing wavelengths.

Students might mistakenly pick option A or B because they represent specific image types formed by a convex lens under limited conditions, ignoring that convex lenses can produce both real and virtual images. Can be real or virtual depending on object position is correct about the image formed by a convex lens. A real, inverted image that can be magnified or diminished is formed when the object is beyond the focal point, such as in a projector. A virtual, erect, and magnified image is formed when the object is between the lens and the focal point, such as in a magnifying glass. Common mistake: assuming a convex lens only creates one type of image regardless of where the object is placed.

Students might mistakenly choose 'Specific heat' because the problem involves copper and temperature changes, but specific heat refers to unit mass rather than the total mass given. Heat capacity is defined as the amount of heat required to raise the temperature of a given mass of a substance by 1 Kelvin or 1°C. Mass multiplied by the specific heat capacity of copper calculates the heat needed to increase the temperature of 10 kg of copper by 1 K, which represents its heat capacity. Heat capacity applies directly to the entire mass rather than per unit mass like specific heat, for phase change like latent heat, or total molecular energy like internal energy. Common mistake: confusing specific heat capacity per unit mass with total heat capacity for a given mass.

A student might incorrectly choose options like 1000 A due to a decimal placement error in the denominator calculation. To find the current, we rely on Faraday’s first law, mass = Z x I x t. Here, the time must first be converted into seconds, giving 5 minutes multiplied by 60 seconds per minute, which equals 300 s. Substituting the known values into the rearranged formula, we divide the mass of 36.0 g by the product of the electrochemical equivalent 0.0012 g/C and the 300 s, resulting in 36 divided by 0.36 to yield a steady current of 100 amperes. Common mistake: failing to convert minutes into seconds before applying the formula.

A student might mistakenly select refraction of light, confusing the bending of rays through a medium with the outright blocking of light. Shadows and eclipses form because light travels strictly in straight lines, a principle known as rectilinear propagation. When an opaque barrier intercepts this path, it stops light from reaching the underlying surface to create a shadow, just as the moon interposes itself to block sunlight during a solar eclipse. This straight-line journey prevents light from wrapping around objects, distinguishing it from reflection or diffraction. Common mistake: confusing the stopping of light by an obstacle with the bending of light waves.

A student might incorrectly select diodes, knowing they are common electronic components but forgetting they have a non-linear voltage-current relationship. Ohm’s Law dictates that voltage remains directly proportional to current, expressed as V = IR at a constant temperature. Metallic conductors like copper and aluminum strictly adhere to this linear behavior under normal operating conditions. For instance, increasing the voltage across a copper wire proportionally increases the current, confirming that metals are ohmic materials compared to non-ohmic components or insulators like glass. Common mistake: assuming all electronic components and circuit materials follow a linear V-I relationship.

A student might mistakenly select a torch battery, assuming smaller portable power sources have less resistance. Internal resistance measures an electrochemical cell's internal opposition to current flow. Rechargeable accumulators like lead-acid car batteries are engineered specifically to deliver massive currents without excessive energy loss, meaning a brand new accumulator possesses the lowest internal resistance among the choices. Common mistake: confusing physical battery size with the magnitude of its internal resistance.

A student might incorrectly choose amplitude, confusing the loudness of a sound wave with its frequency. Pitch relies entirely on frequency, where higher frequencies directly generate higher-pitched tones. Adjusting an acoustic device to vibrate faster—such as raising a string's frequency—shifts the sound higher, just as an 880 Hz note sounds higher than a 440 Hz note. Common mistake: confusing loudness, which is governed by amplitude, with pitch, which is governed by frequency.

A student might mistakenly select the absence of released neutrons, overlooking the fundamental mechanism that sustains the reaction. Nuclear fission begins when a heavy nucleus like uranium-235 splits after absorbing a neutron, yielding both energy and additional free neutrons. These newly liberated neutrons strike other nuclei to trigger subsequent fissions, successfully producing a self-sustaining chain reaction in controlled settings like a nuclear power plant. Common mistake: forgetting that fission events produce the very neutrons required to sustain the reaction.

A student might mistakenly choose 16.03 cm³ by failing to account for volume expansivity instead of linear expansivity. The volume expansivity coefficient, beta, is roughly three times the linear expansivity alpha, giving brass a beta of 3 times 2 times 10^-5, which equals 6 times 10^-5 per degree Celsius. Using the thermal expansion equation, the volume change equals the initial volume of 15.00 cm³ multiplied by beta and the temperature change of 100°C, yielding a delta V of 0.009 cm³. Adding this change to the initial volume gives 15.009 cm³, which rounds to 15.03 cm³. Common mistake: using the linear expansivity directly in the volumetric expansion formula without multiplying it by three.

A student might mistakenly choose 200 J by simply taking the initial kinetic energy of the bullet without accounting for momentum conservation after impact. Assuming a completely inelastic collision where the bullet embeds into the freely moving block, initial momentum is calculated as mass of the bullet multiplied by its velocity, giving 0.05 kg times 200 m/s, which equals 10 kg·m/s. By equating this initial momentum to the total combined mass of 1 kg multiplied by the final velocity, we find the post-impact velocity is 10 m/s. Substituting this final velocity and total mass into the kinetic energy formula yields one-half times 1 kg times 10 squared, resulting in 50 J. Common mistake: calculating kinetic energy using only the bullet's initial mass and speed after the collision occurs.

A student might mistakenly select 70 V by adding the resistor and inductor voltages together instead of recognizing resonance conditions. At resonance in a series R-L-C circuit, the inductive reactance equals the capacitive reactance, making the voltages across the inductor and capacitor equal in magnitude but opposite in phase so they completely cancel each other out. Because the given inductor voltage is 40 V, the capacitor voltage must also be 40 V to maintain this reactive balance. Common mistake: treating reactive voltages as in-phase components that sum up directly.

A student might mistakenly choose 10 years by dividing the total time incorrectly or misinterpreting the exponent. The remaining fraction of a radioactive substance follows the decay relation where the final fraction equals one-half raised to the power of total time divided by half-life. Since the remaining fraction is 1/64 and 64 equals 2 to the sixth power, the ratio of total time to half-life must equal 6. Dividing the total duration of 120 years by 6 yields a half-life of 20 years, meaning the substance halves its quantity six times over that span. Common mistake: dividing the total time by the denominator of the fraction rather than the exponent of two.

A student might mistakenly choose the temperature of the body itself, assuming hotter objects lose heat uniformly regardless of their environment. Newton’s law of cooling establishes that the rate of heat loss depends strictly on the temperature difference separating the body from its surroundings. For example, a hot cup of tea cools much faster in a cold room than in a warm room because a larger temperature gap accelerates the rate at which heat transfers outward. Common mistake: focusing on the absolute temperature of the hot object while ignoring the ambient temperature of its environment.

A student might mistakenly select using both AC and DC sources, confusing grounding safety measures with power supply compatibility. Earthing establishes a direct, low-resistance pathway from the metal casing of an electrical appliance straight into the ground. If an internal fault causes a live wire to touch the casing, this path safely diverts stray current away from anyone touching the appliance, preventing severe electric shocks. Common mistake: believing earthing alters the operational voltage or current type required by the appliance.

A student might mistakenly choose boiling, failing to realize that boiling requires a specific temperature and occurs throughout the liquid, whereas this process happens spontaneously. Evaporation is the spontaneous transition of a liquid into vapor at any temperature below the boiling point, driven by surface molecules escaping into the atmosphere. Water left in an open dish disappears gradually at room temperature through this molecular motion, distinguishing it from boiling or sublimation. Common mistake: confusing the spontaneous surface vaporization at any temperature with boiling at a fixed point.

A student might mistakenly choose relative masses, assuming heavier elements dictate different phases of matter. The fundamental physical differences distinguishing solids, liquids, and gases stem from the spacing and intermolecular forces operating between their molecules. Solids feature tightly packed molecules with powerful binding forces maintaining a rigid shape, liquids possess moderate spacing allowing them to flow, and gases exhibit vast molecular spacing with negligible forces. For instance, ice, liquid water, and steam demonstrate how changing these intermolecular distances alters physical behavior. Common mistake: attributing phase states to molecular mass rather than intermolecular spacing and forces.

A student might mistakenly select magnified or real images, confusing convex mirrors with concave mirrors. Convex mirrors consistently produce images that are erect, virtual, and diminished relative to the actual object. This specific optical behavior allows the mirror to capture a wide-angle view of the surroundings, making them ideal side mirrors for vehicles because they display a smaller, upright view of a broad area behind the car. Common mistake: mixing up the image characteristics of convex mirrors with those of concave mirrors.

A student might mistakenly choose pitch, thinking that playing the same musical note means all acoustic properties are identical. Instruments playing the exact same note are told apart by their quality, also known as timbre. Quality is governed by the unique blend of harmonics and overtones produced, which vary according to the instrument's material and construction, allowing a listener to easily distinguish a violin from a trumpet playing the same pitch. Common mistake: confusing pitch, which identifies the fundamental frequency, with quality, which distinguishes instrument characteristics.

A student might mistakenly choose less current, assuming parallel setups reduce total electrical consumption. In a parallel home circuit, every appliance hooks directly across the main power source so that each device experiences the full supply voltage. This parallel architecture guarantees that appliances receive their required operating voltage and can function independently if another device breaks down. Common mistake: confusing the independent voltage supply of parallel circuits with current-saving assumptions.

A student might mistakenly choose 1 rad/s by directly equating the linear speed to angular velocity without factoring in the radius. Angular velocity is defined as linear velocity divided by the radius of the circular path. Inserting the given linear speed of 1 m/s and the radius of 0.5 m into this relationship gives 1 divided by 0.5, which evaluates to an angular velocity of 2 rad/s. Common mistake: ignoring the radius value when converting linear speed to angular velocity.

A student might mistakenly select 90 N by calculating the ideal effort from the principle of moments but forgetting to account for machine efficiency. Using the lever principle where effort multiplied by the effort arm equals load multiplied by the load arm, the ideal effort equals 180 N multiplied by 1 divided by the effort-to-load arm ratio of 2, giving 90 N. Because the machine operates at an efficiency of 90 percent, the actual effort required is found by dividing the ideal effort by 0.9, resulting in 100 N to overcome energy losses. Common mistake: stopping the calculation at the ideal effort without adjusting for efficiency losses.

A student might mistakenly choose 15 m/s by miscalculating the acceleration product or misapplying the time variable. For an object dropped from rest in free fall, the final velocity is calculated using the equation v = u + gt, where initial velocity u is zero, acceleration due to gravity g is 10 m/s², and time t is 3 seconds. Multiplying gravity by the time yields a final speed of 30 m/s straight downward, assuming air resistance is negligible. Common mistake: dividing instead of multiplying the acceleration by the elapsed time.

A student might mistakenly choose 1000 m/s by multiplying frequency and wavelength incorrectly or treating the decimal as a whole number. Wave speed is determined by multiplying frequency by wavelength. Taking the given frequency of 500 Hz and multiplying it by the wavelength of 0.5 m yields 250 m/s, representing the rate at which the wave travels through the medium. Common mistake: miscalculating the product of a whole number and a decimal fraction.

A student might mistakenly select 2000 J by dropping one of the equation terms during multiplication. The thermal energy required to change a substance's temperature is given by multiplying mass, specific heat capacity, and temperature change together. Here, multiplying the mass of 2 kg by the specific heat capacity of 400 J/kg°C and the temperature change of 5°C yields 4000 J of required heat energy. Common mistake: omitting either the mass or the temperature change factor in the heat equation.

A student might mistakenly select 3 V by inverting the turns ratio in the calculation. For an ideal transformer, the secondary voltage relates to the primary voltage by the turns ratio, where secondary voltage equals primary voltage multiplied by the ratio of secondary turns to primary turns. Given a primary voltage of 12 V and a turns ratio of 800 secondary turns to 200 primary turns, we multiply 12 by 4 to find a stepped-up secondary voltage of 48 V. Common mistake: putting the primary turns over the secondary turns, which would incorrectly step down the voltage.

A student might mistakenly select 10 m due to an arithmetic error in squaring the initial velocity or doubling the acceleration. The maximum height is calculated using the kinematic formula relating final velocity squared to initial velocity squared plus two times acceleration and displacement. Setting final velocity to zero at the peak, we have zero equal to the initial velocity of 20 squared plus two times negative 10 times height, which simplifies to 400 minus 20h equals zero, giving a maximum height of 20 meters. Common mistake: incorrectly handling the negative sign of gravitational acceleration during the rearrangement.

A student might mistakenly choose 2 Ω, assuming the resistance remains unchanged despite physical alterations to the wire. Resistance is proportional to length and inversely proportional to cross-sectional area, expressed as R = ρL/A. When the length doubles, resistance doubles; when the cross-sectional area is halved, resistance doubles again. Multiplying the initial resistance of 2 Ω by these combined factors of 2 and 2 yields a new total resistance of 8 Ω. Common mistake: treating the reduction in cross-sectional area as a decrease rather than an increase in resistance.

A student might mistakenly choose option B (10 kg m/s) by accidentally dividing the mass and velocity rather than multiplying them. To find the correct momentum, compute the product of the body's mass and its velocity. Multiplying the given mass of 5 kg by the velocity of 4 m/s yields 20 kg m/s. This calculated momentum reflects the motion of the body and gauges the precise force needed to alter its direction or bring it to a stop. Common mistake: Dividing the mass by the velocity instead of multiplying them together.

A student might incorrectly select option A (5 D) by failing to convert the focal length from centimeters into meters before applying the formula. Power is calculated as the inverse of the focal length expressed in meters, with diopters serving as the unit. Converting 10 cm yields 0.1 m, and taking its reciprocal produces 10 D. The positive value of 10 diopters highlights the light-bending capability characteristic of a converging convex lens. Common mistake: Forgetting to convert centimeters to meters when calculating lens power.

A student could mistakenly choose option A (100 J) by omitting the squared current value or leaving out one of the multiplication steps in Joule's law. The total heat generated inside a resistor is determined by multiplying the squared current by the resistance and the time interval. With a current of 2 A, resistance of 5 Ω, and a time of 10 seconds, squaring 2 gives 4, which then multiplies by 5 and 10 to total 200 J. This thermal energy is produced through the conversion of electrical energy within the component. Common mistake: Forgetting to square the current value when applying Joule's law.

A student might mistakenly select option C (45 m) by miscalculating the fall time or incorrectly combining the given height and speed values. The horizontal distance relies upon the horizontal speed alongside the exact duration of the fall. Determining time through the free-fall equation h = ½ g t² using a height of 20 m and gravity of 10 m/s² results in t = 2 s, which multiplies by the 15 m/s horizontal velocity to produce 30 m. Thus, the particle travels 30 meters horizontally before hitting the ground. Common mistake: Incorrectly solving the free-fall time equation for the vertical motion.