JAMB Physics 2021 Past Questions & Answers

The slope of a graph is calculated as the change in the vertical axis divided by the change in the horizontal axis. For a displacement-time graph, the slope is the change in displacement divided by the change in time. This ratio is the definition of velocity. Because the question specifies a straight line graph, the slope is constant, which means the object is moving with a constant or uniform velocity.

Common mistake: Students often mistakenly choose uniform acceleration because they confuse the slope of a displacement-time graph with the slope of a velocity-time graph, which is what represents acceleration.

Pressure is defined as force applied per unit area (P = F/A). In this case, the force is the man's weight, which is constant in all the options. To get the greatest or maximum pressure, the area of contact must be the smallest. Standing on the toes of one foot provides the smallest contact area compared to lying down or standing on both feet, thus exerting the greatest pressure.

Common mistake: Students might mistakenly choose option A, thinking that lying flat covers a large area and thus exerts a large pressure, but they forget that pressure is inversely proportional to area.

Physical quantities are either fundamental or derived. Fundamental quantities like mass have base units (e.g., kg), while derived quantities are formed by combining fundamental quantities. Area is derived (length x length), thrust (a force) is derived (mass x acceleration), and pressure is derived (force / area). Since mass is a fundamental quantity, only I, II, and III are derived.

Common mistake: Students often mistakenly choose option A, forgetting that mass is one of the seven fundamental physical quantities and not derived from others.

This problem is solved using the principle of conservation of linear momentum, which states that the total momentum before a collision equals the total momentum after it. The initial momentum is from the first ball (0.5kg * 10ms⁻¹) as the second is at rest, giving a total of 5 kgms⁻¹. After the collision, the two balls move together, so their combined mass is 1.0kg, moving at a common velocity 'v'. By equating the initial momentum to the final momentum $(5 = 1.0 * v)$, we can calculate that the common velocity 'v' is 5.0 ms⁻¹.

Common mistake: Students might mistakenly add the initial velocity and the masses together and divide by two $(e.g., (10 + 0.5 + 0.5) / 2 = 5.5)$, leading them to incorrectly choose option D.

Simple Harmonic Motion (SHM) is a special kind of repetitive back-and-forth movement. For a body to be in SHM, its acceleration must always be directed towards a fixed central point, known as the equilibrium position. This acceleration is also directly proportional to the distance from that point, which means the farther the body moves away, the stronger the pull back to the center. Option A correctly identifies the directional requirement for the acceleration in SHM.

Common mistake: Students often mistakenly choose option D because they remember the acceleration is directed towards a fixed point, but they forget that the magnitude of the acceleration is not constant; it changes, being maximum at the ends and zero at the center.

This question tests the assumptions of the kinetic theory of gases. While it is true that gas molecules are in constant motion (A), have different speeds (B), and their temperature is related to their average kinetic energy (C), the idea that their collisions are perfectly elastic is an assumption for an 'ideal gas'. For real gases, collisions are not perfectly elastic as some kinetic energy can be converted to other forms, making statement D the incorrect one for a general gaseous substance.

Common mistake: Students often memorize that 'perfectly elastic collisions' is a key postulate of the kinetic theory, so they fail to identify it as the incorrect statement because it only applies to ideal gases, not all gases in general.

This question applies the Pressure Law, which states that for a fixed mass of gas at constant volume, pressure is directly proportional to its absolute temperature (P₁/T₁ = P₂/T₂). First, convert the temperatures to Kelvin by adding 273: T₁ = 47°C + 273 = 320 K and T₂ = 27°C + 273 = 300 K. Substitute the values into the formula: $80/320$ = P₂/300. Solving for the new pressure, P₂, gives $(80 × 300)$ / 320 = 75 Nm⁻².

Common mistake: The most common mistake is forgetting to convert the temperatures from Celsius to Kelvin before using the formula, which leads to an incorrect calculation resulting in option A.

The total heat extracted (88000 J) is the sum of the heat lost when cooling the water and the heat lost during freezing. First, calculate the heat lost during cooling from 10°C to 0°C using Q₁ = mcΔθ, which is 0.5kg × 4200 Jkg⁻¹°C⁻¹ × 10°C = 21000 J. The remaining heat, used for freezing, is 88000 J - 21000 J = 67000 J. Finally, calculate the specific latent heat of fusion using Lf = Q₂/m, which is 67000 J / 0.5 kg = 134000 J/kg or 134.0 kJkg⁻¹.

Common mistake: A common mistake is to forget the heat lost during cooling and incorrectly use the total heat extracted (88000 J) to calculate only the latent heat, leading to a wrong answer.

A hygrometer is the scientific instrument specifically designed to measure the amount of water vapour in the air, which is known as humidity. The other options are incorrect; a hydrometer measures the density of liquids, a manometer measures pressure, and a hypsometer measures altitude by checking the boiling point of water. Therefore, to measure relative humidity, a hygrometer is the correct tool to use.

Common mistake: Students often mistakenly choose 'Hydrometer' because its name sounds similar to 'Hygrometer' and both relate to water, but a hydrometer measures the density of liquids, not the humidity of air.

To find the period of vibration, we first need to calculate the frequency of the sound wave using the wave speed formula, v = fλ. Rearranging this gives frequency (f) = speed (v) / wavelength (λ), so f = 330 / 1.65, which equals 200 Hz. The period (T) is the inverse of the frequency (T = 1/f). Therefore, the period is 1 divided by 200, which gives 0.005 seconds.

Common mistake: Students often mistakenly choose 200 s because they correctly calculate the frequency (f = 200 Hz) but forget that the question asks for the period (T), which is the reciprocal of the frequency.

An echo is the reflection of sound. The time given, 0.5s, is the total time for the sound to travel to the cliff and return to the boy. First, calculate the total distance the sound travelled using the formula: Distance = Speed × Time, which is 340 m/s × 0.5s = 170m. Since this total distance is for the sound going and coming back, the actual distance to the cliff is half of this value, which is 170m / 2 = 85m.

Common mistake: The most common mistake is choosing 170m by forgetting that the time given is for the sound to travel to the cliff and back, so the calculated distance must be halved.

A vector quantity is a physical quantity that has both magnitude (size) and direction, while a scalar quantity has only magnitude. Temperature measures the degree of hotness or coldness and is described by a value alone (e.g., 30°C), making it a scalar. Force, momentum, and displacement are all vector quantities because they are incomplete without specifying their direction.

Common mistake: Students may confuse momentum with a scalar quantity like energy, but momentum is a vector because it is the product of mass and velocity, and velocity has direction.

To solve this, you must calculate the heat for two separate processes. First, heat the water from 80°C to its boiling point of 100°C using the formula Q₁ = mcΔT, which gives 50g × 4.2 Jg⁻¹K⁻¹ × $(100-80)K$ = 4,200 J. Second, vaporize the water at 100°C using the formula Q₂ = mL, which gives 50g × 2260 Jg⁻¹ = 113,000 J. The total heat required is the sum of both stages: Q₁ + Q₂ = 4,200 J + 113,000 J = 117,200 J, which is closest to option D, 130,000 J.

Common mistake: A common mistake is to only calculate the latent heat of vaporization (113,000 J) and forget to add the heat required to first raise the water's temperature from 80°C to its boiling point.

In a series R-L-C circuit, the condition for resonance is that the inductive reactance $(X_L)$ is equal to the capacitive reactance $(X_C)$. Because the same current flows through both components, this means the voltage across the inductor $(V_L)$ must be equal to the voltage across the capacitor $(V_C)$. Since the voltage across the inductor is given as 40V, the voltage across the capacitor must also be 40V.

Common mistake: Students often mistakenly use the Pythagorean theorem to combine the resistor and inductor voltages $(√(30² + 40²) = 50V)$, forgetting the specific condition for resonance where inductor and capacitor voltages are equal.

The kinetic energy gained by an electron when accelerated by a potential 'V' is given by KE = eV. This energy is converted into the energy of the emitted X-ray photon, which is given by E = hf. By equating these two energies, we get eV = hf. To find the accelerating potential V, we rearrange the formula to V = hf / e. Substituting the values, V = $(6.63 × 10⁻³⁴ × 1.6 × 10¹⁶)$ / $(1.6 × 10⁻¹⁹)$, which simplifies to 66.3 V.

Common mistake: A common mistake is miscalculating the powers of ten, for example, by subtracting the exponent in the denominator (-19) instead of adding it when it moves to the numerator.

The fraction of a radioactive material remaining is given by the formula $(1/2)ⁿ$, where 'n' is the number of half-lives that have passed. In this question, the fraction left is $1/64$, so we set $(1/2)ⁿ$ = $1/64$. Since 64 is 2 raised to the power of 6 (2⁶), it means that 6 half-lives have occurred. If 6 half-lives took a total of 120 years, we find the duration of one half-life by dividing the total time by the number of half-lives, which is 120 years / 6 = 20 years.

Common mistake: Students might incorrectly calculate that 2⁵ = 64 instead of 2⁶ = 64, leading them to divide 120 by 5 to get the wrong answer of 24 years.

Beta rays are streams of fast-moving electrons, which are negatively charged particles. Because they have a charge, they are deflected when they pass through an electric field. Similarly, a magnetic field exerts a force on any moving charge, so beta rays are also deflected by a magnetic field, unlike gamma rays which are uncharged.

Common mistake: Students often mistakenly choose gamma rays because they are a common type of radiation, but they forget that gamma rays are uncharged and therefore cannot be deflected by electric or magnetic fields.

A pair of vernier calipers is the correct instrument because it has special inner jaws designed to measure the internal diameter of objects like pipes or test tubes. These jaws are inserted into the opening and expanded to touch the inner walls, allowing for a direct and accurate reading. A meter rule is not precise enough for this small measurement, and a micrometer screw gauge is used for external diameters, not internal ones.

Common mistake: Students often mistakenly choose the micrometer screw gauge because it is known for high accuracy, but they forget that its design is for measuring external dimensions, not internal ones like the inside of a test tube.

According to Newton's second law of motion, Force is the product of mass and acceleration (F = ma). To find the ratio of the two forces (F₁ : F₂), we multiply their respective mass and acceleration ratios: F₁/F₂ = (m₁/m₂) × (a₁/a₂). Substituting the given values, we get F₁/F₂ = $(3/1)$ × $(2/9)$ = $6/9$. Simplifying this fraction by dividing both numbers by 3 gives $2/3$, so the ratio of the forces is 2:3.

Common mistake: A common mistake is to correctly calculate the proportional force values (6 and 9) but then form the ratio incorrectly, for instance by comparing the first force to the difference between the forces (6:3), which simplifies to 2:1 (Option B).

The centripetal force is the force that keeps an object moving in a circular path. It is calculated using the formula F = mω²r, where 'm' is the mass, 'ω' is the angular velocity, and 'r' is the radius. Substituting the given values, we get F = (10⁻² kg) × (100 rad/s)² × (0.2 m), which simplifies to F = 0.01 × 10000 × 0.2 = 20 N.

Common mistake: Students might misread the radius as 2m instead of 0.2m, leading them to incorrectly calculate the force as 200N (Option C).

First, we use the principle of conservation of momentum to find the final velocity of the bullet and block stuck together. The total momentum before impact (m₁u₁) equals the total momentum after impact ((m₁+m₂)v), which gives a final velocity of 10 m/s. Then, we calculate the final kinetic energy using the formula KE = ½mv², with the total mass (0.05kg + 0.95kg = 1.0kg) and this final velocity, resulting in ½ × 1.0kg × (10m/s)² = 50J.

Common mistake: Students often correctly find the final velocity but then forget the '½' in the kinetic energy formula (KE = ½mv²), leading them to incorrectly calculate 100J.

According to the principle of conservation of energy, the total energy remains constant throughout the motion since air resistance is ignored. The total energy is the sum of potential energy (P.E.) and kinetic energy (K.E.). At the top of the tower, P.E. = mgh = 0.1 x 10 x 10 = 10J, and K.E. = ½mv² = ½ x 0.1 x 10² = 5J. Therefore, the total energy is 10J + 5J = 15J.

Common mistake: A common mistake is to calculate only the initial potential energy (10J) or only the initial kinetic energy (5J), forgetting that total energy is the sum of both.

Power is the rate at which work is done, calculated as Work Done divided by Time. In this case, the work done on the car is equal to its gain in kinetic energy (KE). First, find the kinetic energy using the formula KE = ½mv², which is ½ × 800kg × (25m/s)² = 250,000 Joules. Then, divide this work done by the time taken to find the power: Power = 250,000 J / 20 s = 12,500 W, or 1.25 × 10⁴W.

Common mistake: Students might mistakenly calculate power by multiplying the force by the final velocity (P = Fv), which leads to an incorrect answer of 2.50 × 10⁴W.

When a car is moving forward and the brakes are applied, the frictional force between the tyres and the road acts in the opposite direction to the motion. This opposing force is what causes the car to slow down and eventually stop. Because stopping the car is the desired outcome, this frictional force is considered a major advantage for safety.

Common mistake: Students may mistakenly choose option B because they have learned that friction is often a disadvantage that causes wear and tear, failing to recognize its essential and advantageous role in braking.

First, we find the strain, which is the change in length divided by the original length. The change in length is 10.05m - 10.00m = 0.05m. So, the strain is 0.05m / 10.00m = 0.005. Next, we use the formula for Young's modulus, which is Stress / Strain. Plugging in the values, we get 10⁷ Nm⁻² / 0.005, which equals 2 × 10⁹ Nm⁻².

Common mistake: A common mistake is to divide the stress by the extension (0.05m) instead of the strain (0.005), which results in an answer that is off by a factor of ten.