Post-UTME Physics 2006 Past Questions & Answers

Power is the rate of doing work, which is calculated as Work divided by Time. In this problem, the work done is the potential energy gained by the man, calculated as mass × g × height. Using g as 10m/s², Work = 70kg × 10m/s² × 4m = 2800 Joules. Then, Power = 2800J / 7s = 400W. It appears there is an error in the question's provided correct option, as the calculated answer is 400W (Option D). To arrive at the given answer of 40W (Option A), the calculation would have incorrectly omitted the acceleration due to gravity (g), making it $(70 × 4)$ / 7 = 40W.

Common mistake: The most common mistake is to correctly include acceleration due to gravity (g ≈ 10m/s²) in the work formula (Work = mgh), which leads to the physically correct but unintended answer of 400W (Option D).

First, calculate the maximum velocity reached after accelerating from rest using the formula v = u + at. With initial velocity u=0, acceleration a=6ms⁻², and time t=8s, the maximum velocity is v = 6 * 8 = 48ms⁻¹. This becomes the initial velocity for the deceleration phase. To find the deceleration, we use the same formula where the body comes to rest (final velocity v=0) in 5s: 0 = 48 + (a * 5). Solving for 'a' gives $-48/5$ = -9.6ms⁻², so the magnitude of the deceleration is 9.6ms⁻².

Common mistake: Students might mistakenly choose 48ms⁻² because it is the correct maximum velocity reached after the acceleration phase, but they forget to use this value to calculate the final deceleration.

The effective force used to pull the nail is the component of the tension acting perpendicular (straight out) from the wall. Since the angle given is 30° to the wall (the vertical), the perpendicular component is found using the sine function. Therefore, the effective force is Tension × sin(30°), which is 50N × 0.5, giving a result of 25N.

Common mistake: Students often mistakenly use the cosine function, calculating 50N × cos(30°) to get $25√3$ N, because they confuse the angle to the wall with the angle to the horizontal.

The formula for gravitational potential (V) at a distance 'r' from the center of a mass 'M' is V = -GM/r. In this problem, the point is at an altitude 'H' above the Earth's surface, which has a radius 'R'. Therefore, the total distance 'r' from the center of the Earth to that point is the sum of the radius and the altitude, so r = R + H. Substituting this into the formula gives the potential as V = –GM/(R+H).

Common mistake: Students often mistakenly use only the altitude H as the distance 'r' from the mass, leading them to incorrectly choose option A, because they forget that gravitational distance is measured from the center of the celestial body.

The Mechanical Advantage (MA) of any machine is defined as the ratio of the Load to the Effort. The Velocity Ratio (VR) is defined by the geometry of the machine, which for an inclined plane is the ratio of its length to its height (l/h). Although for a smooth (ideal) inclined plane the MA is equal to the VR, the property that is fundamentally defined by the ratio of length to height is the Velocity Ratio. Therefore, the statement that the Mechanical Advantage depends on this ratio is considered technically untrue, as this is the definition of Velocity Ratio.

Common mistake: Students often mistakenly choose option B, as it seems intuitive that a steeper, harder-to-climb plane would be less efficient, but this is not necessarily the case.

To solve this, we set up a proportion relating the Celsius scale to the thermometer's millimeter scale using the formula: (Reading - Lower Point) / (Upper Point - Lower Point). This gives us (75°C - 0°C) / (100°C - 0°C) = (Ymm - 20mm) / (100mm - 20mm). Simplifying the equation, we get $75/100$ = (Y - 20)/80, which means 0.75 = (Y - 20)/80. Solving for Y, we find Y = $(0.75 * 80)$ + 20, which equals 60 + 20 = 80mm.

Common mistake: Students might calculate the change in length from the ice point $(0.75 * 80mm = 60mm)$ but forget to add it to the initial ice point reading of 20mm, mistakenly choosing 60mm.

To solve this, you must understand that the electrical energy supplied by the kettle is converted into heat energy absorbed by the water. First, calculate the heat energy (Q) needed using the formula Q = mcΔθ, which is Q = 2kg × 4200 J/kgK × (100°C - 20°C) = 672,000 Joules. Since Electrical Energy = Power × time, we can find the time by rearranging the formula to time = Energy / Power, so time = 672,000 J / 2000 W = 336 seconds.

Common mistake: Students might mistakenly choose option C if they forget to multiply by the mass of the water (2kg) in the heat energy calculation, which results in calculating the time for only 1kg of water.

To find the total heat supplied, you must calculate the heat for three stages: heating the ice from -10°C to 0°C, melting the ice into water at 0°C, and finally heating the water from 0°C to 90°C. These steps require the specific heat capacities of ice and water, and the specific latent heat of fusion. Since the final temperature is 90°C, the water does not boil, so the specific latent heat of vaporization (for turning water to steam) is not required.

Common mistake: Students might mistakenly choose 'specific latent heat of fusion' if they forget that for ice to reach 90°C, it must first melt into water, a process which requires this constant.

Diffusion is the movement of particles from an area of high concentration to an area of low concentration. The perfume molecules, after evaporating, are highly concentrated near the jar and then spread out into the rest of the room by mixing with the air molecules. This movement is due to the random motion of the gas particles, which is a key concept in the kinetic theory of gases.

Common mistake: Students often confuse diffusion with evaporation; evaporation is the process of the liquid perfume turning into a gas, while diffusion is how the gas scent then spreads through the air.

First, use the magnification formula, m = v/u. Since the image is half the size of the object, the magnification m = $1/2$, which gives u = 2v. Next, substitute this into the lens formula, 1/f = 1/u + 1/v, using the given focal length f = 10cm. This gives $1/10$ = 1/(2v) + 1/v, which simplifies to $1/10$ = 3/(2v). Solving for the image distance 'v' gives 2v = 30, so v = 15cm.

Common mistake: Students might correctly calculate both the object distance (u=30cm) and image distance (v=15cm) but then add them together to get 45cm (Option A), misinterpreting the question as asking for the total separation between the object and image.