JAMB Physics 2014 Past Questions & Answers

A standard meter rule has its smallest markings in millimeters (mm), so its least count is 1 mm. The least possible error, also known as the precision, for any measuring instrument is taken as half of its smallest division. Therefore, for a meter rule, the least possible error is half of 1 mm, which is 0.5 mm.

Common mistake: Students often mistakenly choose 1.0mm because they confuse the least possible error with the least count (smallest division) of the meter rule.

This question asks for the definition of a vector quantity. A vector quantity is a physical quantity that requires both magnitude (size) and direction to be fully described. Displacement is the correct answer because it is defined as the distance moved in a specific direction, making it a vector. The other options like temperature, distance, and mass are scalar quantities because they only have magnitude and no direction.

Common mistake: Students often mistakenly choose 'Distance' because it is closely related to displacement, but they forget that distance is a scalar quantity that does not have a specified direction.

A vector quantity is a physical quantity that has both magnitude (size) and a specific direction, while a scalar quantity only has magnitude. Torque is a turning force that has a direction (e.g., clockwise or anti-clockwise), and momentum is the product of mass and velocity, which also has a direction. Electrical potential and kinetic energy are forms of energy, and energy is a scalar quantity because it does not have a direction. Therefore, only torque (II) and momentum (IV) are vectors.

Common mistake: Students often mistakenly choose an option including kinetic energy, because they associate it with motion, forgetting that energy itself is a scalar quantity without direction.

The wheels of a moving car undergo two types of motion at the same time. As the car moves forward from one point to another, the wheels also move forward, which is called translational motion. Simultaneously, the wheels are spinning around their centre or axle, and this is known as rotational motion. Therefore, the complete motion of the wheels is a combination of both translational and rotational motion.

Common mistake: Students might mistakenly choose option A because they think of the bumps on the road causing vibration, but the fundamental and primary types of motion for a wheel on a moving car are translational and rotational.

To solve this problem, we use one of the equations of motion for uniform acceleration, which is v² = u² + 2as. The car starts from rest, so its initial velocity (u) is 0. The acceleration (a) is given as 3 m s⁻² and the distance (s) is 24 m. Substituting these values, we get v² = 0² + 2 * 3 * 24, which simplifies to v² = 144. Taking the square root of both sides gives the final velocity (v) as 12 m s⁻¹.

Common mistake: Students might mistakenly choose 144 m s⁻¹ because they calculate v² correctly but forget to take the square root to find the final velocity, v.

To calculate the escape velocity (vₑ), you use the formula vₑ = $√(2gR)$, where 'g' is the acceleration due to gravity and 'R' is the radius of the earth. Assuming g is approximately 10 m/s² and using the given radius R = 6.4 x 10⁶ m, we get vₑ = $√(2 * 10 * 6.4 x 10⁶)$. This simplifies to vₑ = $√(128 x 10⁶)$ which is approximately 11314 m/s, and converting to km/s by dividing by 1000 gives 11.3 km/s.

Common mistake: A common mistake is forgetting the factor of '2' in the formula, which is equivalent to calculating the orbital velocity $(v = √gR)$ instead of the escape velocity.

First, understand that the question gives the mass of the object as 8kg, even though it incorrectly calls it 'weight'. Weight is calculated using the formula: Weight = mass × acceleration due to gravity (W = mg). On the new planet, gravity is one-third of Earth's gravity, so the weight will also be one-third of the weight on Earth. Using g on Earth as approximately 10 m/s², the weight on the planet is (8 kg × 10 m/s²) / 3 = 80 / 3 ≈ 26.7 N, which is closest to 27 N.

Common mistake: Students often get confused by the incorrect phrasing 'weight of 8kg' and may perform a wrong calculation instead of first finding the object's weight on Earth (about 80 N) before dividing by three.

Equilibrium means that an object is not accelerating, so its acceleration is zero. According to Newton's second law of motion, Force = mass × acceleration (F=ma). If the acceleration is zero, then the total or net force acting on the object must also be zero. This 'net force' is the same as the 'vector sum of the forces', which is why it must be zero for an object to be in equilibrium.

Common mistake: Students might mistakenly choose 'Positive' or 'Negative' if they only consider forces acting in one direction, but for equilibrium, the forces in all directions must balance out completely to result in zero.

For an object to be balanced (in equilibrium) under the action of three forces that are not parallel, two conditions must be met: the net force must be zero, and the net turning effect (torque) must also be zero. To ensure the net torque is zero, the lines of action of all three forces must intersect at a single common point. If they did not meet at one point, the forces would create a turning effect, and the object would start to rotate, meaning it would not be in equilibrium.

Common mistake: Students might mistakenly choose option A because they recall that parallel forces can also be in equilibrium, but they overlook the key phrase 'non-parallel' in the question.

According to the principle of conservation of energy, the potential energy of the object at the highest point is converted into kinetic energy just before it hits the ground. We calculate the initial potential energy using the formula P.E. = mgh, where m is mass, g is acceleration due to gravity (take g = 10 m/s²), and h is height. Therefore, the kinetic energy is 20 kg × 10 m/s² × 10 m, which equals 2000 Joules.

Common mistake: Students might mistakenly calculate only mass times height $(20 x 10 = 200J)$, forgetting to include the acceleration due to gravity (g) in the potential energy formula, leading to the incorrect option A.

The energy stored in the nucleus of an atom is called nuclear energy. In a nuclear power plant, processes like nuclear fission release this energy as a massive amount of heat. This heat is then used to boil water and produce steam, which drives a turbine connected to a generator to produce electrical energy for our homes and industries.

Common mistake: Students might mistakenly choose 'Mechanical energy' because they know the heat is used to turn a turbine, which is a form of mechanical energy, but they forget that this is just an intermediate step before the generator converts it into the final product, which is electrical energy.

The efficiency of a machine is given by the formula: Efficiency = (Mechanical Advantage / Velocity Ratio). First, we find the Mechanical Advantage (M.A.) using the given values: M.A. = Efficiency × Velocity Ratio = 0.75 × 4 = 3. Next, we use the formula for Mechanical Advantage, which is M.A. = Load / Effort. To find the effort, we rearrange the formula to Effort = Load / M.A., which gives us 1000N / 3 = 333.33N.

Common mistake: A common mistake is to calculate the ideal effort (Load / V.R. = 250N) and then incorrectly multiply by the efficiency, forgetting that an inefficient machine requires more effort, not less.

The efficiency of a machine is calculated by dividing its Mechanical Advantage (M.A.) by its Velocity Ratio (V.R.) and multiplying by 100%. First, the M.A. is the Load (800N) divided by the Effort (250N), which equals 3.2. The V.R. for a wheel and axle is the radius of the wheel (800mm) divided by the radius of the axle (200mm), which equals 4. Therefore, the efficiency is $(3.2 / 4)$ x 100%, which gives 80%.

Common mistake: A common mistake is to incorrectly calculate the Velocity Ratio by dividing the smaller radius (axle) by the larger one (wheel), leading to an impossible efficiency value.

Tensile stress is calculated using the formula: Stress = Force ÷ Area. In this question, the force applied is 500 N and the cross-sectional area is 0.2 m². So, the stress is 500 N / 0.2 m², which equals 2500 N m⁻². To write this in standard form (scientific notation), we get 2.5 × 10³ N m⁻².

Common mistake: Students might mistakenly multiply the force and area $(500 × 0.2 = 100)$ instead of dividing, leading them to incorrectly choose option B.

Dew is formed through a process called condensation, which is a change of state from gas to liquid. During the night, surfaces like grass cool down, and if their temperature drops to the 'dew point', the water vapour in the air that comes in contact with them turns into liquid water droplets. This is a classic example of a change of state.

Common mistake: Students often confuse dew with mist or fog, but mist and fog are tiny water droplets suspended in the air, while dew forms directly on a surface.

To convert a temperature from the Kelvin scale (K) to the Celsius scale (°C), you use the formula: °C = K - 273. In this question, the temperature in Kelvin is 20 K. So, substituting this value into the formula gives °C = 20 - 273, which equals –253 °C.

Common mistake: Students may mistakenly add 273 to the Kelvin temperature instead of subtracting, leading them to calculate 293 and then incorrectly choose the negative version, –293 °C.

Charles' Law describes the relationship between the volume and temperature of a gas at constant pressure. The law states that volume (V) is directly proportional to absolute temperature (T), which is written mathematically as V/T = constant. This can be rearranged as V¹T⁻¹ = constant. For the general equation PᵃVᵇTᶜ = constant to represent this, the pressure (P) must be constant, so its power 'a' must be 0. Comparing V¹T⁻¹ = constant to the remaining VᵇTᶜ = constant, we see that b=1 and c=-1.

Common mistake: Students often mistakenly choose option C, thinking that direct proportionality (V ∝ T) means VT = constant, when it actually means V/T = constant.

Heat capacity is defined as the quantity of heat energy required to raise the temperature of an entire body or object by 1 Kelvin. The question is a direct statement of this definition. Unlike specific heat capacity, it considers the whole body, not just a unit mass of it.

Common mistake: Students often mistakenly choose 'Specific heat capacity' because it is a very similar concept, but they forget that specific heat capacity refers to raising the temperature of a unit mass (e.g., 1kg) of the substance, not the entire body.

Melting point is the specific temperature at which a substance changes from a solid to a liquid. Solidification, or freezing, is the opposite process where a liquid changes back to a solid. For any pure substance, the temperature for melting and the temperature for freezing are exactly the same, so the melting point is equivalent to the solidification temperature.

Common mistake: Students might be confused by the term 'Liquidification Temperature' because melting involves turning into a liquid, but 'solidification temperature' is the correct scientific term for the reverse process which occurs at the same temperature.

The dew point is the exact temperature to which air must be cooled for it to become saturated with water vapour. If the temperature drops any further below the dew point, the excess water vapour will condense into liquid water, which we see as dew. Therefore, it is the temperature at which the water vapour present is just enough to saturate the air.

Common mistake: Students often confuse this with 'Saturation point', but 'Saturation point' describes the condition of being saturated, while 'Dew point' is the specific name for the temperature at which this condition is reached.

Convection is the transfer of heat through the actual movement of a fluid, like a liquid or gas. When a liquid is heated, it expands, its volume increases, and it becomes less dense. This lighter, hotter liquid rises, while the cooler, denser liquid from the top sinks to take its place, creating a continuous circulation called a convection current that transfers heat.

Common mistake: Students often confuse convection with conduction, incorrectly choosing 'Increased vibration of the molecules' which is the primary mechanism for heat transfer in solids.

The relationship between wave velocity (v), frequency (f), and wavelength (λ) is given by the formula v = fλ. The distance between successive crests is the wavelength, so λ = 15 cm, which must be converted to 0.15 m to match the units of velocity. Rearranging the formula to find frequency gives f = v / λ, so f = 300 m/s / 0.15 m = 2000 Hz, which is written as 2.0 × 10³ Hz in standard form.

Common mistake: A common mistake is forgetting to convert the wavelength from centimeters to meters before calculation, which leads to an incorrect answer.

An echo is a reflected sound wave. The time given (0.8 s) is for the sound to travel to the hill and return to the boy. First, we calculate the total distance travelled by the sound using the formula distance = speed × time, which gives 340 m/s × 0.8 s = 272 m. Since this total distance is for the journey to the hill and back, the distance to the hill is half of this value, which is 272 m / 2 = 136 m.

Common mistake: The most common mistake is forgetting to divide the calculated total distance by two, as students often fail to account for the fact that the echo time represents a two-way trip.

Linear magnification is calculated by dividing the image distance by the object distance (m = v/u). The image distance (v) is the length of the pinhole camera, 25cm, and the object distance (u) is 10m. To calculate correctly, you must first convert both values to the same unit, so we change 25cm to 0.25m. Now, divide the image distance by the object distance: m = 0.25m / 10m = 0.025. Expressing 0.025 in standard form gives 2.5 × 10⁻², which is the correct answer.

Common mistake: The most common mistake is failing to convert the object distance (m) and image distance (cm) to the same unit before dividing, leading to an incorrect calculation.

To find the image position, we use the mirror formula: 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance. Given f = 2.0 cm and u = 8.0 cm, we rearrange the formula to find v: 1/v = 1/f - 1/u. Substituting the values, we get 1/v = $1/2.0$ - $1/8.0$, which simplifies to 1/v = $(4 - 1)/8.0$ = $3/8.0$. Therefore, v = $8.0/3$ cm, which is approximately 2.67 cm, making 2.7 the closest numerical answer.

Common mistake: A common mistake is to calculate 1/v = $3/8$ and forget to take the reciprocal to find the final value for v, which is $8/3$.