JAMB Physics 2009 Past Questions & Answers

A micrometer screw gauge is a precision instrument designed to measure very small lengths or thicknesses with high accuracy, usually up to 0.01mm. The diameter of a small ball bearing and the thickness of a piece of paper are both very small dimensions, making the micrometer the perfect tool for the job. A measuring cylinder's diameter is too large for a micrometer, and the length of a wire is best measured with a ruler or tape measure.

Common mistake: Students often mistakenly choose option A, forgetting that while a micrometer is used for a wire's tiny diameter, it is not suitable for measuring its overall length.

Acceleration is the gradient (or slope) of a velocity-time graph. To find the gradient, you divide the change in velocity (the 'rise') by the change in time (the 'run'). Using the given points, the change in velocity is 35 m/s - 15 m/s = 20 m/s, and the change in time is 20 s - 10 s = 10 s. Therefore, the acceleration is 20 m/s divided by 10 s, which equals 2.00 m/s².

Common mistake: A common mistake is to divide the final velocity (35 m/s) by the final time (20 s), which gives 1.75 m/s², leading to the incorrect selection of option A.

This problem involves motion under gravity. At its maximum height, the final velocity (v) of the bullet is 0 m/s. We can find the initial velocity (u) using the first equation of motion: v = u + at, where acceleration 'a' is -g because the bullet is moving upwards against gravity. Substituting the values, we get 0 = u + (-10 m/s² * 4.0 s), which simplifies to 0 = u - 40, making the initial velocity u = 40 m/s.

Common mistake: Students might get confused by the '2.0 m above the ground' information, which is a distractor and not needed to calculate the initial velocity.

Simple Harmonic Motion (SHM) is a special to-and-fro or oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position. A loaded test tube oscillating in a liquid, the motion of a piston in an engine, and the beating of the heart (as a biological approximation) are all examples of this type of motion. The motion of a car tyre is rotational and translational, while a stone whirled round is in circular motion, neither of which is SHM.

Common mistake: Students often mistakenly include the stone whirled round (IV), confusing uniform circular motion with Simple Harmonic Motion because both are periodic.

First, calculate the work done to lift the coal using the formula for potential energy, Work = mgh, which gives 750 kg × 10 m/s² × 90 m = 675,000 J. Next, calculate power by dividing the work by the time in seconds (1 minute = 60 s), so Power = 675,000 J / 60 s = 11,250 W. Converting to kilowatts gives 11.25 kW; the provided correct option of 12.60 kW likely results from a typo in the question's original values, as a mass of 840 kg would yield that answer.

Common mistake: A common mistake is forgetting to convert the time from one minute to 60 seconds before calculating the power.

To find the coefficient of static friction (μ), we use the formula F = μR, where F is the limiting frictional force and R is the normal reaction. The frictional force is equal to the applied force required to start motion, so F = 500 N. The normal reaction (R) on a horizontal surface is equal to the object's weight (mg), which is 80 kg × 10 m/s² = 800 N. Therefore, the coefficient of friction is μ = F / R = 500 N / 800 N = 0.625, and the closest given option is 0.6.

Common mistake: A common mistake is to confuse the values, for example, by assuming the mass is 50 kg, which makes the normal reaction 500 N and leads to an incorrect coefficient of 1.0 (Option C).

The velocity ratio (V.R.) of an inclined plane is a measure of how much the machine multiplies the distance moved by the effort. The formula for the V.R. of an inclined plane is 1 divided by the sine of the angle of inclination (V.R. = 1/sinθ). For an angle of 30°, sin(30°) is 0.5, so the velocity ratio is 1 / 0.5, which equals 2.0.

Common mistake: Students might mistakenly calculate sin(30°) which is 0.5, instead of the correct formula for velocity ratio which is 1 divided by sin(30°).

The pressure in a liquid is calculated using the formula P = hρg, where 'h' is the depth, 'ρ' is the density, and 'g' is the acceleration due to gravity. This formula shows that pressure is directly affected by the liquid's density (I) and acceleration due to gravity (II). The shape or type of the container (III) does not appear in the formula and therefore does not affect the pressure at a given depth. Similarly, while the constituents of the liquid (IV) determine its density, it is the density value itself, not the specific chemical makeup, that directly influences pressure.

Common mistake: Students often mistakenly think the constituents of the liquid affect pressure, forgetting that it is the resulting density of the liquid, not its chemical makeup, that is the direct factor in the pressure formula (P = hρg).

The work done in stretching an elastic cord is calculated using the formula for elastic potential energy, which is Work Done = ½ × Force × extension. First, you must convert the extension from centimeters to meters: e = 1.2 cm = 0.012 m. Then, substitute the values into the formula: Work Done = ½ × 10 N × 0.012 m = 0.06 J. In standard form, this is written as 6.0 × 10⁻² J.

Common mistake: A common mistake is to calculate work done as simply Force × extension, forgetting the ½ factor which is required because the force applied is not constant but increases from 0 to 10 N.

According to the principle of flotation, the weight of a floating object is equal to the weight of the fluid it displaces. Since the same sphere floats in both liquids, the weight of the displaced water must equal the weight of the displaced glycerine. Using the formula: (Volume submerged × density of fluid) × g, we can set up the equation: $(0.50 × V × ρ_water)$ = $(0.40 × V × ρ_glycerine)$. The volume V cancels out, leaving 0.50 × 1000 kg/m³ = 0.40 × $ρ_glycerine$, which gives the density of glycerine as 500 / 0.40 = 1250 kg/m³.

Common mistake: Students often mistakenly calculate the density of the plastic sphere itself (500 kg m⁻³) and select that answer, instead of continuing to find the density of the glycerine as required.

An optical pyrometer is a special thermometer used for measuring very high temperatures of objects from a distance, such as molten steel in a furnace. It works based on the principle that the color of a glowing hot object changes as its temperature changes, from red to orange to white-hot. By comparing the color of the hot body to a calibrated scale, its temperature can be accurately determined.

Common mistake: Students might mistakenly choose the thermocouple because it is also used for high-temperature measurements, but it operates on the principle of generating a voltage (Seebeck effect), not by observing a change in color.

Water has a special property called anomalous expansion. Unlike most substances that continuously shrink when cooled, water's volume decreases only until it reaches 4°C. At this temperature, it has its smallest or minimum volume and is at its most dense. If you cool it further from 4°C to 0°C, it will start to expand again.

Common mistake: Students might mistakenly choose 'maximum' because they know ice (at 0°C) is less dense and takes up more volume than water, but they forget that the point of maximum density (and minimum volume) occurs at 4°C.

First, calculate the total electrical energy supplied by the heater, which is converted into heat energy. Electrical Energy = Power × time = 1000 W × 300 s = 300,000 J. This heat energy is then absorbed by the water, causing its temperature to rise, according to the formula Q = mcΔθ. By equating the electrical energy to the heat absorbed, we get 300,000 = m × 4200 × $(100 - 30)$. Solving for the mass (m) gives m = 300,000 / $(4200 × 70)$, which equals approximately 1.02 kg.

Common mistake: A common mistake is to use the final temperature (100 °C) instead of the change in temperature (100 °C - 30 °C = 70 °C) in the calculation, which leads to an incorrect answer.

The boiling point of a liquid is defined as the specific temperature at which its saturated vapour pressure becomes equal to the external atmospheric pressure. When this condition is met, the liquid begins to change into gas (boil) throughout its volume. Therefore, if the vapour pressure on the liquid equals the atmospheric pressure, the liquid is at its boiling point.

Common mistake: Students might mistakenly choose 'standard temperature' because they confuse the conditions for boiling with the standard conditions (STP) used in gas law calculations.

To find the time, first calculate the total heat energy needed to boil off the water using the formula Q = mass × specific latent heat of vaporization (Q = mL). This gives Q = 2 kg × 2.3 × 10⁶ J/kg = 4.6 × 10⁶ J. Since the heater's power is the energy it supplies per second (Power = Energy/time), the time taken is the total energy divided by the power. Therefore, time = 4.6 × 10⁶ J / 1000 W = 4.6 × 10³ s.

Common mistake: Students may choose option C by making a calculation error with the powers of ten, for example, dividing by 100 instead of the correct power of 1000 W.

This question is about the forces between molecules, a topic often discussed with fluids and pressure. Adhesion is the force of attraction between different types of molecules (like water and glass), while cohesion is the force between similar molecules (like water and water). For water to spread out and 'wet' the glass surface, its molecules must be pulled more strongly towards the glass than towards each other. This means the force of adhesion (water-glass) must be greater than the force of cohesion (water-water).

Common mistake: Students often confuse the definitions of adhesion and cohesion, or they might choose an option that describes the opposite scenario (like for mercury), where cohesion is stronger than adhesion.

Heat is transferred in three ways: conduction, convection, and radiation. Radiation is the transfer of heat through electromagnetic waves, which can travel through empty space or air. Since the man is standing at a distance from the fire, the primary way heat reaches him is through these waves. Convection involves the movement of hot air, which mostly rises upwards from the fire, and conduction requires direct contact, which is not happening here.

Common mistake: Students often mistakenly choose convection because they know fire heats the air, but they forget that convection currents primarily move upwards, while radiation travels outwards in all directions.

Sound is a mechanical wave that travels at different speeds in different media. Its speed is highest in solids, lower in liquids, and lowest in gases. Because metal cables are solids, sound travels through them at a very high speed, making them effective for transmitting sound signals over long distances with minimal delay.

Common mistake: Students may mistakenly choose option C, incorrectly believing that a lower speed is better or confusing the properties of solids with gases where sound travels slowest.

The quality of a musical note, also known as timbre, is the characteristic that distinguishes between different instruments playing the same note at the same loudness. While the pitch (determined by the fundamental frequency) is the same, each instrument produces a unique combination of overtones or harmonics. This unique blend of frequencies is what our ears perceive as the instrument's specific sound quality.

Common mistake: Students often mistakenly choose 'pitch' because a note is associated with a specific pitch, but the question states the instruments are already playing the same note, meaning their fundamental pitch is the same.

Natural sources of light are objects that produce their own light and are not man-made. The Sun and other stars produce their own light through nuclear reactions, making them natural sources. The Moon does not produce its own light but shines by reflecting sunlight, so it is not a source. A street light is an artificial, man-made source of light.

Common mistake: Students may mistakenly choose an option that includes the Moon, forgetting that it is a natural object but not a natural source of light as it only reflects sunlight.

To find the image distance, 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 = 10 cm and u = 5 cm, we substitute these values to get $1/10$ = $1/5$ + 1/v. Solving for 1/v gives 1/v = $1/10$ - $1/5$ = $-1/10$, which means v = -10 cm. The negative sign indicates that the image is virtual and formed behind the mirror, so the image is 10 cm behind the mirror.

Common mistake: Students often calculate the magnitude correctly but forget that the negative sign for the image distance (v) means the image is virtual and located behind the mirror, not in front of it.

To solve this, we use the mirror formula: 1/f = 1/u + 1/v. For a convex mirror, the focal length (f) and image distance (v) are virtual, so we give them negative signs. Therefore, f = -12 cm and v = -6 cm. Rearranging the formula to find the object distance (u), we get 1/u = 1/f - 1/v, which becomes 1/u = 1/(-12) - 1/(-6). This simplifies to 1/u = $-1/12$ + $2/12$ = $1/12$, so u = 12.0 cm.

Common mistake: Students often choose option A (4.0 cm) by incorrectly using a positive value for the image distance (v = +6 cm) instead of the correct negative value (v = -6 cm) for a virtual image.

The critical angle (c) is related to the refractive index (n) by the formula sin(c) = 1/n. Given that the refractive index of crown glass is 1.51, we can substitute this value into the formula. This gives us sin(c) = 1 / 1.51, which is approximately 0.6623. To find the angle c, we calculate the inverse sine (arcsin) of 0.6623, which results in an angle of 41.5°.

Common mistake: Students might guess option D (45.0°) because it is a common angle in physics problems, especially if they cannot recall the correct formula relating critical angle and refractive index.

The speed of light in a medium is inversely related to its refractive index (n), meaning a higher refractive index leads to a lower speed of light. Medium x has a higher refractive index (1.51) compared to medium y (1.33). Therefore, light travels slower in medium x and faster (has a higher speed) in medium y.

Common mistake: Students often mistakenly believe that a higher refractive index means a higher speed of light, leading them to incorrectly choose option C.

The human eye contains a natural convex lens that focuses light onto the retina. Accommodation is the special process where the ciliary muscles change the curvature and focal length of this lens. This adjustment allows the eye to form a clear image of objects at different distances, whether they are near or far.

Common mistake: Students may mistakenly choose options like 'interference' or 'diffraction' because they are properties of light, but they do not describe the eye's specific mechanism for focusing.