JAMB Physics 2013 Past Questions & Answers

Mass is the measure of the amount of matter in an object, and it is a fundamental property that does not change with location. Weight, on the other hand, is the force of gravity acting on that mass (Weight = mass x g). Because the moon has a weaker gravitational pull than the earth, the brick's weight would reduce, but its mass remains constant.

Common mistake: Students often confuse mass with weight; they know gravity is weaker on the moon, so they incorrectly choose option B, thinking the mass reduces when it is actually the weight that reduces.

Imagine the resultant force (50N) as the hypotenuse of a right-angled triangle, with the two perpendicular forces as the other two sides. The question asks for the force that makes a 30° angle with the resultant, which is the side adjacent to this angle. Using trigonometry, the adjacent side is calculated as Hypotenuse × cos(angle). Therefore, the force is 50 N × cos(30°), which equals 50 × 0.866, giving 43.3 N.

Common mistake: Students often mistakenly use the sine function instead of cosine, calculating 50 N × sin(30°) = 25.0 N, which finds the magnitude of the other perpendicular force, not the one requested.

This question tests your knowledge of scalar and vector quantities. Scalar quantities are physical quantities that have only magnitude (size), while vector quantities have both magnitude and direction. Volume and area are both scalars because they are fully described by a number and a unit, without needing a direction. The other options are incorrect because they each contain at least one vector quantity like momentum, displacement, or impulse.

Common mistake: Students often confuse length with displacement in option C, but displacement is a vector because it specifies distance in a particular direction.

The period of a simple pendulum, T, is related to its length, L, by the relationship T² is proportional to L (T² ∝ L). This means we can set up a ratio: (T₂/T₁)² = L₂/L₁. Given T₁ = 2s, L₁ = 0.4m, and L₂ = 0.8m, we substitute these values to get (T₂/2)² = $0.8/0.4$, which simplifies to (T₂/2)² = 2. Taking the square root of both sides gives T₂/2 = $√2$, so the new period T₂ is $2√2$ s.

Common mistake: A common mistake is to assume the period is directly proportional to the length (T ∝ L), leading students to incorrectly double the period to 4s when the length is doubled.

This question uses the first equation of motion, which is v = u + at. Here, the initial velocity (u) is 20 ms⁻¹, the final velocity (v) is 0 ms⁻¹ because the train comes to a halt, and the acceleration (a) is -2 ms⁻² since it is decelerating. Substituting these values into the formula gives 0 = 20 + (-2)t, which simplifies to 2t = 20. Therefore, the time (t) required is 20 divided by 2, which equals 10 seconds.

Common mistake: Students might incorrectly choose 40s by mistakenly multiplying the initial velocity by the deceleration (20 x 2) instead of using the correct equation of motion.

This problem is about forces and acceleration, which is an application of Newton's Second Law of Motion. The apparent weight loss is the force responsible for the man's downward acceleration. This force is calculated by multiplying the man's mass by the elevator's acceleration (F = ma). Therefore, the apparent weight loss is 70 kg × 1.5 ms⁻², which gives 105 N.

Common mistake: Students often mistakenly choose 595 N because they correctly calculate the apparent weight (m(g-a)) but fail to find the apparent weight *loss* as the question requires.

According to the principle of flotation, the fraction of an object's volume immersed in a fluid is equal to the ratio of the object's density to the fluid's density. To find the fraction, we divide the density of the cork by the density of the liquid. This gives $(0.25 × 10³ kgm⁻³)$ / $(1.25 × 10³ kgm⁻³)$, which simplifies to 0.25 / 1.25, resulting in 0.2.

Common mistake: A common mistake is to calculate the fraction of the volume that is *above* the liquid $(1 - 0.2 = 0.8)$, which incorrectly leads to option A.

This question requires you to equate the potential energy (PE) of the stationary body with the kinetic energy (KE) of the moving body. The formula for PE is mgh and for KE is ½mv². Setting them equal, mgh = ½mv², the mass 'm' cancels out, leaving gh = ½v². Using the given velocity v = 5 m/s and taking g as 10 m/s², we find the height h = v² / (2g) = 5² / $(2 * 10)$ = 25 / 20 = 1.25 m, which is approximately 1.3 m.

Common mistake: Students might mistakenly calculate only the square of the velocity (5² = 25) and choose 25.0 m, confusing an intermediate calculation with the final answer for height.

First, calculate the work done by the pump to lift the water, which equals the potential energy gained (Work = mgh). Next, convert the time from minutes to seconds $(15 min × 60 = 900 s)$. Using g ≈ 9.8 m/s², the work done is 5000 kg × 9.8 m/s² × 60 m = 2,940,000 J. Finally, power is the work done divided by time, so Power = 2,940,000 J / 900 s ≈ 3267 W, which is best represented as 3.3 × 10³ Js⁻¹.

Common mistake: A common mistake is forgetting to convert the time from minutes to seconds before calculating the power, which would lead to an incorrect answer.

The work done in stretching a spring is calculated using the formula W = ½Fe, where F is the force and e is the extension. First, you must convert the extension from millimeters (mm) to meters (m) by dividing by 1000, so 50mm becomes 0.05m. Substituting the given values into the formula, we get W = ½ × 20N × 0.05m, which equals 0.5 Joules (J).

Common mistake: Students often mistakenly calculate work as simply force multiplied by distance (W = F × e), forgetting the ½ factor which accounts for the average force applied while stretching the spring.