Post-UTME Physics 2009 Past Questions & Answers

The S.I. system has seven fundamental units which are the basic building blocks for all other physical units. These include the Ampere (for electric current), Kelvin (for temperature), and seconds (for time). The radian, however, is a derived unit used for measuring angles and is not one of the seven fundamental S.I. units.

Common mistake: Students might mistakenly choose Ampere, thinking it is derived from other quantities like charge and time (I=Q/t), but it is officially defined as a fundamental S.I. unit.

The centre of gravity is the balance point of the system, which is found using the principle of moments. Let the centre of gravity be a distance 'x' from the heavier 60g mass, so its distance from the lighter 40g mass is (100 - x) cm. For the system to balance, the clockwise moment must equal the anticlockwise moment: 60g * x = 40g * (100 - x). This simplifies to 100x = 4000, which gives x = 40cm from the heavier mass.

Common mistake: Students often calculate the distance from the lighter mass (which is 60cm) but then incorrectly select the option that matches that number to the wrong mass, like '60cm from the heavier mass'.

The time given (1 second) is for the sound wave to travel to the bottom of the sea and return to the ship as an echo. First, calculate the total distance travelled using the formula: distance = velocity × time, which gives 1500 m/s × 1 s = 1500 m. Since this distance is for the round trip (down and back up), the actual depth of the sea is half of this total distance, which is 1500 m / 2 = 750 m. Converting this to kilometers gives 0.75 km.

Common mistake: Students often forget that the echo time is for the sound to travel down and back up, so they mistakenly choose 1.50km (1500m) as the answer without dividing by two.

The efficiency of a machine is calculated as (Mechanical Advantage / Velocity Ratio) x 100%. First, find the Mechanical Advantage (M.A.), which is the ratio of Load to Effort, so M.A. = 200kg / 50kg = 4. Since the Velocity Ratio (V.R.) is given as 5, the efficiency is $(4 / 5)$ x 100%, which equals 80%.

Common mistake: Students often make a mistake by incorrectly calculating the Mechanical Advantage as Effort divided by Load $(50/200)$ instead of Load divided by Effort, which leads to the wrong answer of 5%.

Electric field intensity is defined as the force experienced per unit charge in an electric field. The formula is E = F/q, where E is the electric field intensity, F is the force, and q is the charge. Using the values given, E = 4N / 0.2C, which calculates to 20 N/C.

Common mistake: Students often mistakenly multiply the force and the charge $(4 x 0.2 = 0.8)$ instead of dividing, which leads them to incorrectly choose option B.

The resistance of a wire is given by the formula R = ρL/A, where L is the length and A is the cross-sectional area (which depends on the diameter). The resistivity, ρ, is a property of the material which also changes with temperature. Therefore, resistance depends on the length, the diameter (area), and the temperature of the wire, making 'All of the above' the correct option.

Common mistake: Students often mistakenly choose only option A because the direct relationship between resistance and length (R ∝ L) is the most commonly remembered factor.

A dry cell is a source of electrical energy. While the traditional Leclanché dry cell uses a paste of ammonium chloride as its electrolyte, modern alkaline batteries, which are also a type of dry cell, use potassium hydroxide instead. Therefore, since not all dry cells contain ammonium chloride, it is the component that is not always present. The other options, a carbon rod, a zinc case, and a depolarizing paste (manganese dioxide, not magnesium dioxide), are more fundamental components.

Common mistake: The most common mistake is recalling only the classic Leclanché cell from textbooks, which does contain ammonium chloride, leading students to incorrectly eliminate that option.

A yellow card appears yellow because it reflects red and green light, while absorbing blue light. A blue glass acts as a filter that only allows blue light to pass through it, absorbing other colours like red and green. When you look at the yellow card through the blue glass, the red and green light reflected from the card is completely absorbed by the glass, so no light reaches your eye, making the card appear black.

Common mistake: Students might mistakenly choose 'green' because they are thinking of mixing yellow and blue paint, but the physics of light filters works by subtracting colours, not by mixing them like pigments.

A microphone is a transducer specifically designed to capture sound energy and convert it into electrical energy. When sound waves strike the microphone's diaphragm, it vibrates, and this mechanical motion is then transformed into an electrical signal that represents the original sound.

Common mistake: Students might mistakenly choose the telephone earpiece because it also involves sound and electricity, but it performs the opposite energy conversion, changing electrical energy back into sound energy.

The relationship between the velocity (v), frequency (f), and wavelength (λ) of a wave is given by the formula v = fλ. To find the wavelength, we rearrange the formula to λ = v / f. Given the velocity v = 3 x $10^8$ m/s and frequency f = 800 kHz $(which is 800,000 Hz or 8 x 10^5 Hz)$, we can calculate the wavelength. So, λ = $(3 x 10^8)$ / $(8 x 10^5)$ = 0.375 x $10^3$ m, which equals 375m.

Common mistake: A common mistake is failing to correctly convert the frequency from kilohertz (kHz) to hertz (Hz), which can lead to a calculation error and the selection of an incorrect option like 37.5m.

Heat can be transferred in three ways: conduction, convection, and radiation. Conduction happens through solids, and convection happens through fluids (liquids and gases), so both require a material medium. Radiation, however, transfers heat using electromagnetic waves, which can travel through a vacuum or empty space. This is how we feel the heat from the sun, even though it has to travel through the vacuum of space to reach us.

Common mistake: Students often confuse conduction and convection with radiation, but they should remember that both conduction (in solids) and convection (in fluids) require particles to transfer heat, unlike radiation.

This problem assumes a simplified linear model where pressure decreases uniformly with height. The pressure at ground level (0 km) is 760 mmHg and at the top (80 km) is 0 mmHg. The pressure at any height is due to the weight of the air column ABOVE it. The height of the air column above 20 km is 80 km - 20 km = 60 km. Therefore, the pressure at 20 km is (60 km / 80 km) × 760 mmHg = $(3/4)$ × 760 mmHg = 570 mmHg. NOTE: The provided correct option 'C' (190 mmHg) is physically incorrect for this model, as it represents the pressure drop over 20km, not the pressure AT 20km. This indicates a flawed question, but the topic classification remains 'Pressure'.

Common mistake: The most common mistake is to assume pressure is directly proportional to the height from the ground, calculating $(20/80)$ * 760 = 190 mmHg, which incorrectly leads to option C.

For a simple pendulum, the period (T) is proportional to the square root of its length (L), so the relationship is T₁/T₂ = $√(L₁/L₂)$. Given T₁ = 1.55s, L₁ = 0.6m, and L₂ = 0.4m, we can set up the equation: 1.55 / T₂ = $√(0.6 / 0.4)$ = $√(3/2)$. Solving for T₂ gives T₂ = 1.55 / $√(3/2)$, which is approximately 1.27s. Since this calculated value is not available in options A, B, or C, the correct choice is D.

Common mistake: Students often forget the square root in the formula and may incorrectly assume a simple direct or inverse relationship between period and length, leading to a wrong answer.

Both evaporation and boiling are processes where a liquid changes into a gas, which is known as vaporization. Evaporation occurs when molecules escape from the surface of the liquid. In boiling, bubbles of vapour form throughout the liquid, rise, and then break at the surface. Therefore, the final point where vapour escapes into the air is the surface for both processes.

Common mistake: The most common mistake is choosing option C; while it is true that both involve a change of state, this question's intended answer focuses on the physical location where the vapour ultimately leaves the liquid.

First, find the total energy used in kilowatt-hours (kWh). Convert the power from 200 watts to 0.2 kilowatts (by dividing by 1000) and the time from 20 days to 480 hours (20 days × 24 hours/day). Multiply them to get the energy: 0.2 kW × 480 h = 96 kWh. Finally, calculate the cost by multiplying the total energy by the price per unit: 96 kWh × 5 kobo/kWh = 480 kobo, which is equal to N4.80.

Common mistake: The most common mistake is calculating the cost as 480 kobo and then incorrectly selecting N480.00, forgetting to convert kobo to Naira by dividing by 100.

To find the resistivity (ρ), you use the formula that relates it to resistance (R), cross-sectional area (A), and length (L), which is R = ρL/A. Rearrange the formula to make resistivity the subject: ρ = (R × A) / L. By substituting the given values of R = 0.45 Ω, A = 0.2 x 10⁶ m², and L = 5 m, you can calculate the resistivity of the wire's material.

Common mistake: A common mistake is incorrectly rearranging the formula, for instance, calculating ρ = RL/A instead of ρ = RA/L, which will always lead to a wrong answer.

A pure tone is a sound that has only one single frequency. A tuning fork is a special instrument made to vibrate at a specific, constant frequency when you hit it, which is why it produces a pure tone. Instruments like guitars produce a main frequency plus many other higher frequencies called overtones, which gives them a rich sound but means the tone is not pure.

Common mistake: Students often choose 'Vibrating String' because they know it produces sound, but they forget that it creates a complex sound with multiple frequencies (overtones), not a single-frequency pure tone.

A compound microscope's objective lens must be a converging (convex) lens, which always has a positive focal length, so option A is wrong. To achieve high magnification, the objective lens must also have a very short focal length. Comparing the remaining options, +5mm is much shorter than +5cm (which is equal to +50mm), making it the most suitable choice.

Common mistake: Students may choose +5cm, correctly identifying the need for a positive focal length but failing to select the shortest possible focal length required for high magnification.

Pressure (P) is defined as Force per unit Area, so its unit is Newtons per square meter (N/m²). Volume (V) has a unit of cubic meters (m³). When you multiply the units of P and V, you get (N/m²) × (m³) = N·m. Work or Energy is defined as Force × distance, and its unit is also the Newton-meter (N·m), which is equivalent to the Joule. Therefore, the product PV has the same unit as energy.

Common mistake: Students often confuse the symbol 'P' for Pressure with the symbol 'P' for Power, leading them to incorrectly choose option B.

Weight is defined as the gravitational force acting on an object due to a large body like the Earth. It is calculated by multiplying the object's mass (m) by the acceleration due to gravity (g), using the formula W = mg. Therefore, the force with which the earth attracts an object is correctly called its weight.

Common mistake: Students often mistakenly choose 'gravity' because it is the phenomenon causing the attraction, but 'weight' is the correct scientific term for the actual force exerted on the object.

The refractive index (n) is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v), so the formula is n = c/v. To find the velocity in the liquid (v), we rearrange the formula to v = c/n. By substituting the given values, we get v = (3.0 x 10⁸ m/s) / 1.5, which calculates to 2.0 x 10⁸ m/s. Note that the provided correct option 'D' is physically incorrect as it implies light travels faster in the liquid than in a vacuum; the correct answer is Option B.

Common mistake: A common mistake is to incorrectly multiply the speed of light by the refractive index (3.0 x 10⁸ * 1.5), which leads to the wrong answer of 4.5 x 10⁸ m/s.

To solve this problem, we use the first equation of motion, which is v = u + at. Here, 'v' is the final velocity we want to find, 'u' is the initial velocity (44m/s), 'a' is the acceleration (-4m/s²), and 't' is the time (10s). Substituting the values into the formula, we get v = 44 + $(-4 * 10)$, which simplifies to v = 44 - 40. Therefore, the final velocity of the train after 10 seconds is 4m/s.

Common mistake: A common mistake is to ignore the negative sign for the acceleration and add 40m/s to 44m/s, which would incorrectly suggest the train is speeding up.

Power is the rate at which work is done, calculated as Power = Work / Time. First, we find the work done against gravity, which is the potential energy gained (Work = mass × g × height). So, Work = 50kg × 10m/s² × 5m = 2500 Joules. Then, we divide this work by the time taken to find the power: Power = 2500 J / 5 s = 500 Watts.

Common mistake: Students might correctly calculate the work done as 2500 Joules but then mistakenly divide by the acceleration due to gravity (10) instead of the time (5), leading to the incorrect answer of 250W.

The frequency (f) of a vibrating string is inversely proportional to the square root of its mass (m) when length and tension are constant, so f ∝ $1/√m$. This means the mass is inversely proportional to the square of the frequency, or m ∝ 1/f². If the frequencies are in the ratio f₁:f₂ = 4:1, then the masses will be in the ratio m₁:m₂ = (1/f₁²):(1/f₂²) = $(1/4²):(1/1²)$ = $1/16:1$. Therefore, the ratio of the masses is 1:16.

Common mistake: Students often forget that mass is inversely proportional to the *square* of the frequency, mistakenly choosing 1:4 by ignoring the square in the relationship.