JAMB Physics 2012 Past Questions & Answers

Parallax error happens when you look at a measurement scale from an angle, which makes the reading appear shifted from its true position. To get an accurate reading from a metre rule, your eye must be positioned directly and vertically above the marking. This ensures your line of sight is perpendicular to the scale, preventing any apparent shift and giving you the correct measurement.

Common mistake: Students might choose options A or B if they don't understand that viewing the scale from any slant or angle, whether to the left or right, is precisely what causes parallax error.

Since the load is pulled at a uniform speed, it is not accelerating, which means all the horizontal forces are balanced. The force pulling the load forward is the horizontal component of the rope's tension, which must be equal to the opposing frictional force. We calculate this horizontal component as $F_horizontal$ = 1500N × cos(45°), which gives 1500 × 0.7071, approximately 1061N.

Common mistake: A common mistake is to forget to resolve the force into its horizontal component, as only the horizontal part of the force acts directly against friction.

To solve this problem, we use one of the equations of motion: v² = u² + 2as. Here, the initial speed (u) is 30ms⁻¹, the final speed (v) is 0ms⁻¹ because the train comes to rest, and the acceleration (a) is -0.1ms⁻² since it is a retardation. Substituting these values gives 0² = 30² + 2(-0.1)s, which simplifies to 0 = 900 - 0.2s. Solving for the distance (s) gives s = 900 / 0.2, which equals 4500m.

Common mistake: Students often make a mistake by forgetting that retardation is a negative acceleration, which leads to an incorrect calculation.

To find the distance covered, we use the equation of motion: s = ut + ½at². Since the car starts from rest, the initial velocity (u) is 0. We are given the acceleration (a) as 30ms⁻² and the time (t) as 20s. Plugging these values into the formula, we get s = $(0 * 20)$ + ½ * 30 * (20)², which simplifies to s = 15 * 400 = 6000 metres. To match the options, we convert metres to kilometres by dividing by 1000, which gives us 6km.

Common mistake: A common mistake is forgetting the '½' in the formula s = ut + ½at², which would lead to an incorrect calculation of 12km (Option B).

According to Newton's law of universal gravitation, the force of attraction (F) between two bodies is inversely proportional to the square of the distance (r) between them. This means that as the distance 'r' gets smaller, the force 'F' gets larger. The formula is F = G(m₁m₂)/r², which clearly shows that if the denominator 'r' reduces, the value of the force 'F' will increase.

Common mistake: Students often mistakenly choose option D, thinking that force increases as distance increases, but the law describes an inverse square relationship, not a direct one.

The oscillation described is an example of Simple Harmonic Motion (SHM). A key condition for an object to perform SHM is that its acceleration is directly proportional to its displacement from the equilibrium position and is always directed towards it. This relationship ensures a restoring force always tries to bring the object back to the center, causing it to oscillate.

Common mistake: Students often mistakenly choose option D, confusing the equilibrium point with a point of rest; in reality, the object's velocity is maximum at the equilibrium point and zero at the extreme ends of the swing.

To find the angular velocity, we use the formula that connects linear speed (v) and angular velocity (ω), which is v = ωr, where 'r' is the radius of the circular path. We need to find ω, so we rearrange the formula to be ω = v / r. Substituting the given values, we get ω = 1ms⁻¹ / 0.5m, which equals 2 rads⁻¹.

Common mistake: Students might mistakenly choose option D by confusing angular velocity with the given linear speed, forgetting to account for the radius in the calculation.

For an object on the verge of sliding down an inclined plane, the component of its weight pulling it down the slope (mg sinθ) is equal to the limiting static friction (μN). The normal reaction (N) is equal to the component of weight perpendicular to the slope (mg cosθ). Therefore, mg sinθ = μ * mg cosθ, which simplifies to μ = tanθ. For an angle of 30°, the coefficient of friction μ = tan(30°) ≈ 0.577, which is closest to 0.6.

Common mistake: A common mistake is to use sin(30°) = 0.5 directly, forgetting that the coefficient of friction depends on the ratio of the parallel and perpendicular forces, which simplifies to tanθ.

Efficiency is calculated as the ratio of useful work output to the total work input, expressed as a percentage. First, find the useful work output, which is the work done on the load: Work Output = Load × distance = 250N × 30m = 7500J. The total work input is the sum of the useful work and the work done against friction: Work Input = 7500J + 1500J = 9000J. Finally, calculate the efficiency: Efficiency = (Useful Work Output / Total Work Input) × 100% = $(7500 / 9000)$ × 100% = 83.33%, which is approximately 83.30%.

Common mistake: A common mistake is to calculate the work input incorrectly, for example by subtracting the work done against friction from the useful work output instead of adding them together.

This question applies Hooke's Law, which states that Force (F) equals the force constant (k) multiplied by the extension (e), so F = ke. First, calculate the force (weight) of the load: F = mass × g = 1 kg × 10 m/s² = 10 N. Next, you must convert the extension from centimeters to meters: e = 1.2 cm = 0.012 m. Finally, rearrange the formula to find the force constant: k = F / e = 10 N / 0.012 m = 833.33 N m⁻¹, which is approximately 833 N m⁻¹.

Common mistake: The most common mistake is forgetting to convert the extension from centimeters (cm) to meters (m) before performing the calculation, which leads to a numerically incorrect answer.

Apparent weight is the actual weight of an object minus the upthrust it experiences when in a fluid, according to Archimedes' principle. First, calculate the actual weight: Weight = mass × g = 2 kg × 10 m/s² = 20 N. Next, calculate the upthrust: Upthrust = density of liquid × volume of object × g = 1 kgm⁻³ × 1 m³ × 10 m/s² = 10 N. Finally, the apparent weight is the actual weight minus the upthrust, which is 20 N - 10 N = 10 N.

Common mistake: A common mistake is to calculate only the real weight of the object (20 N) and forget to subtract the upthrust from the liquid, leading to the incorrect choice A.

The pressure in a liquid is calculated using the formula P = hρg, where 'h' is the depth, 'ρ' is the density of the liquid, and 'g' is the acceleration due to gravity. Since 'g' is constant for a given location, the pressure depends directly on the depth 'h' and the density 'ρ' of the liquid. This is why option A is the correct answer.

Common mistake: Students might mistakenly choose option B because density is calculated from mass and volume, but pressure depends on the density as a single property, not the individual mass and volume of the entire liquid.

According to Archimedes' principle, the upthrust on the balloon is equal to the weight of the air it displaces. To find this weight, we use the formula: Upthrust = Volume of displaced air × Density of air × acceleration due to gravity (g). Plugging in the given values, we get Upthrust = 300 m³ × 1.3 kg m⁻³ × 10 m s⁻², which equals 3900 N.

Common mistake: Students might mistakenly calculate the upthrust by only multiplying the volume by gravity $(300 x 10 = 3000 N)$, forgetting to include the density of the displaced air in the calculation.

A clinical thermometer is the specific type used to measure human body temperature. It contains mercury, a liquid metal, inside a sealed glass tube. When the thermometer is placed in a warm area like under the tongue, the mercury absorbs heat, expands, and rises up the narrow tube to show the temperature reading on a scale.

Common mistake: Students might confuse it with an alcohol thermometer, which is also a liquid-in-glass type, but clinical thermometers specifically use mercury because it is more accurate for the narrow range of human body temperatures.

The increase in length of a material is found by multiplying its linear expansivity (α), original length (L), and the change in temperature (Δθ). To find the ratio for P to Q, we divide the formula for P by the formula for Q, which gives $(α_P/α_Q)$ × $(L_P/L_Q)$ since the temperature change is the same for both. Substituting the given ratios, we get $(2/3)$ × $(3/4)$, which simplifies to $6/12$ or $1/2$, resulting in a final ratio of 1:2.

Common mistake: Students may incorrectly invert the ratio of the lengths, calculating $(2/3)$ × $(4/3)$ to get 8:9, which leads to the wrong option C.

This problem is solved using the combined gas law, which states (P₁V₁)/T₁ = (P₂V₂)/T₂. First, convert the initial temperature to Kelvin: T₁ = 27°C + 273 = 300 K. The standard temperature and pressure (s.t.p.) values are T₂ = 273 K (0°C) and P₂ = 760 mmHg. By rearranging the formula to find the new volume (V₂), we get V₂ = (P₁V₁T₂) / (P₂T₁). Substituting the values gives V₂ = (700 x 2000 x 273) / (760 x 300), which calculates to 1676.3 cm³.

Common mistake: Students often make the mistake of using the temperature values in Celsius instead of converting them to the absolute Kelvin scale, which is required for all gas law calculations.

To find the temperature change, we use the formula for quantity of heat, Q = mcΔθ, where Q is heat, m is mass, c is specific heat capacity, and Δθ is the temperature change. First, you must convert the mass from grams to kilograms by dividing by 1000, so 100 g becomes 0.1 kg. Rearranging the formula to find the temperature change (Δθ), we get Δθ = Q / (mc). Substituting the given values, we have Δθ = 500 / $(0.1 × 4200)$, which simplifies to 500 / 420, giving a result of approximately 1.19 °C, which is rounded to 1.2 °C.

Common mistake: The most common mistake is forgetting to convert the mass from grams (g) to kilograms (kg) before calculating, as the specific heat capacity is given in J kg⁻¹ K⁻¹.

Evaporation is the process where water molecules escape from the surface of a liquid. An increase in atmospheric pressure pushes down on the water's surface, making it more difficult for the molecules to escape. Therefore, increasing the pressure actually slows down or decreases the rate of evaporation, it does not increase it. The other options, like a rise in temperature, directly increase the kinetic energy and speed of the molecules, which helps them evaporate faster.

Common mistake: Students sometimes forget that higher atmospheric pressure pushes down on the liquid's surface, which traps the water molecules and slows down evaporation.

To find the total heat energy, you must complete two steps. First, you must heat the ice from -30 °C to its melting point at 0 °C using the formula Q₁ = mcΔθ, which gives 1 kg × $(2.1 × 10³ J/kg°C)$ × 30°C = 63,000 J. Second, you must melt the ice at 0 °C using the latent heat formula Q₂ = mL, which gives 1 kg × $(3.5 × 10⁵ J/kg)$ = 350,000 J. The total heat required is the sum of both amounts: 63,000 J + 350,000 J = 413,000 J, which is 4.13 × 10⁵ J.

Common mistake: A common mistake is to only calculate the heat required for the phase change (melting) and forget to add the heat needed to first raise the ice's temperature from -30 °C to 0 °C.

Brownian motion is the random, zig-zag movement of particles suspended in a fluid, which can be a liquid or a gas. This motion is caused by the constant and uneven collision of these particles with the much smaller, invisible molecules of the fluid. This observation provides strong evidence for the kinetic theory of matter, which states that molecules exist (II) and are in a constant state of random motion (IV). Statement III is incorrect because the motion happens in both liquids and gases, not just gases.

Common mistake: Students often mistakenly believe that Brownian motion only occurs in gases because it is a key concept in the kinetic theory of gases, forgetting that it was first famously observed with pollen grains in water (a liquid).

The standard equation of a wave is y = A sin(2πft - 2πx/λ), where λ is the wavelength. First, expand the given equation: y = 15 sin ( (2π * 60t / 5) - (2πx / 5) ). By comparing the 'x' part of this equation, (2πx/5), with the standard form, (2πx/λ), we can see that 1/λ is equal to $1/5$. Therefore, the wavelength λ is 5 m.

Common mistake: A common mistake is to confuse the amplitude of the wave, which is the number 15 in front of the sin function, with the wavelength.

The velocity of sound is affected by the medium it travels through. Wind is the movement of air, which is the medium for sound. If the wind is blowing in the same direction as the sound, it helps to carry the sound waves along, making them travel faster relative to the ground. Properties of the sound itself, like pitch (frequency) and loudness (amplitude), do not change the speed of sound.

Common mistake: Students often mistakenly believe that increasing the loudness (amplitude) or pitch (frequency) of a sound will make it travel faster, but these properties do not affect the wave's speed through its medium.

The intensity of a wave or vibration is a measure of the energy it carries. This energy is directly proportional to the square of the amplitude, which is the maximum displacement of the vibrating particles from their rest position. Therefore, a vibration with a larger amplitude carries more energy and has a higher intensity.

Common mistake: Students often mistakenly choose Frequency because they confuse intensity (which relates to loudness in sound) with pitch, which is determined by the frequency of the vibration.

A concave mirror is used for shaving because it can produce a magnified and upright image. For this to happen, the object, which is the man's face, must be placed between the principal focus (F) and the pole (P) of the mirror. This specific position is the only one that creates a virtual, erect, and enlarged image, allowing the man to see a bigger and clearer view of his face.

Common mistake: Students often mistakenly choose option A because they remember it produces a magnified image, but they forget that the image formed is inverted (upside down) and therefore not suitable for shaving.

A pinhole camera's magnification is given by the formula: Image height / Object height = Image distance / Object distance. First, we must use consistent units, so we convert the image distance to 0.05 m and the image height to 0.025 m. Substituting the values gives: 0.025 / Object height = 0.05 / 300. Solving for the object height (the building) gives $(0.025 * 300)$ / 0.05, which calculates to 150 m.

Common mistake: Students often make a mistake by not converting all measurements to the same unit (e.g., meters) before calculation, or by making a simple arithmetic error which could lead to an incorrect option like 50 m.