JAMB Physics 2008 Past Questions & Answers

This question tests your knowledge of standard international (S.I.) units for different physical quantities. The S.I. unit for Force is the Newton (N), and for Torque, it is the Newton-meter (Nm). Similarly, the S.I. unit for electric Current is the Ampere (A), and for Power, it is the Watt (W). Since all four pairings of quantity and unit are correct, option D is the right answer.

Common mistake: Students might incorrectly choose option C if they are not confident that the Watt (W) is the correct S.I. unit for Power, perhaps confusing it with other energy-related units like the joule.

A vector quantity is a physical quantity that has both magnitude (size) and a specific direction. For example, acceleration (like 9.8 m/s² downwards), displacement (like 10 meters north), and weight (a force acting towards the center of the Earth) are all vectors. Altitude, on the other hand, simply describes height above a certain level and does not have an associated direction, which makes it a scalar quantity.

Common mistake: Students might mistakenly choose 'weight' because they confuse it with mass, but weight is a force that always has a direction (downwards), making it a vector.

To find the velocity of the wheel, we first need its radius, which is half the diameter $(1.2 m / 2 = 0.6 m)$. The wheel's speed of rotation is given as 1 revolution per second, which is its frequency (f). We use the formula for linear velocity, v = 2πfr. Substituting the values, we get v = 2 * π * 1 * 0.6 = 1.2π, which calculates to approximately 3.77 ms⁻¹.

Common mistake: A common mistake is to use the diameter (1.2 m) instead of the radius (0.6 m) in the calculation, which leads to an incorrect answer of approximately 7.5 ms⁻¹.

For a body to be in equilibrium, it must not move or rotate. This requires two main conditions: the net force must be zero, and the net moment (turning effect) must be zero. Statement II (upward force equals downward force) is part of the first condition, while Statement III (sum of moments is zero) is the second condition. For the special case of three coplanar forces, they must also all meet at a single point to be in equilibrium, which is what 'concurrent' means (Statement I). Therefore, all three conditions are correct.

Common mistake: Students often choose option C because they correctly remember the two general conditions for equilibrium but forget the specific theorem which states that three coplanar forces in equilibrium must also be concurrent.

Frequency is the number of complete cycles or revolutions that happen in one second. To find the frequency, you use the formula: Frequency = Number of revolutions / Time taken. In this question, the balance wheel makes 90 revolutions in 25 seconds, so the frequency is 90 divided by 25, which equals 3.6 Hertz (Hz).

Common mistake: A common mistake is to calculate the period instead of the frequency by incorrectly dividing the time by the number of revolutions $(25 ÷ 90)$.

By the principle of conservation of energy, the initial kinetic energy, E = $(1/2)mu²$, is equal to the sum of potential and kinetic energy at any height h. The question requires the height where potential energy (PE = mgh) is equal to kinetic energy (KE). At this point, the total energy is PE + KE = PE + PE = 2PE = 2mgh. Equating the initial energy to the energy at this height, we get $(1/2)mu²$ = 2mgh. Solving for h gives h = u² / 4g.

Common mistake: Students often mistakenly calculate the maximum height (h = u²/2g), which is the point where all kinetic energy has been converted to potential energy, instead of the height where the two energies are equal.

Adhesion is the force of attraction between molecules of different substances. When counting currency, the moisture (water) on the fingers sticks to the paper notes because of the adhesive force between water molecules and paper molecules. This increased grip makes it easier to pick up and separate a single note from the stack.

Common mistake: Students often confuse adhesion with cohesion; cohesion is the force of attraction between molecules of the *same* substance (like water sticking to water), not between different substances like water and paper.

For the motorcycle to move in a circle, the force of friction between the tyres and the road provides the necessary centripetal force. The formula for centripetal force is Fc = mv²/r, and the formula for friction is Ff = μmg. By equating these two forces (mv²/r = μmg), we can find the coefficient of friction (μ), which gives μ = v² / (rg). Substituting the values (v=5, r=10, and g≈10) gives μ = 5² / $(10 × 10)$ = 25 / 100 = 0.25.

Common mistake: Students often mistakenly calculate only the centripetal acceleration (a = v²/r = 2.5) and select it as the answer, forgetting to divide by the acceleration due to gravity (g) to find the coefficient of friction.

The energy stored in a spring is calculated using the formula E = ½ke², where 'k' is the force constant and 'e' is the compression. First, you must convert the compression from centimeters to meters, so 5 cm becomes 0.05 m. Substituting the values into the formula gives E = ½ × 500 × (0.05)², which calculates to 0.625 J.

Common mistake: Students often make a mistake by not converting the compression from centimeters to meters, or by converting it incorrectly (e.g., using 0.5m instead of 0.05m), which leads to an incorrect answer like 62.5 J.

The Hare's apparatus works on the principle that the pressure exerted by the two liquid columns is the same. Since pressure in a fluid is given by P = hρg, we can say $h_water$ * $ρ_water$ = $h_liquid$ * $ρ_liquid$. The relative density of the liquid is the ratio of its density to the density of water $(ρ_liquid / ρ_water)$. Rearranging the formula, we get Relative Density = $h_water$ / $h_liquid$, which is 26.5 cm / 20.4 cm = 1.299, approximately 1.3.

Common mistake: A common mistake is to incorrectly divide the liquid's height by the water's height $(20.4 / 26.5)$, which leads to the wrong answer of 0.8.