JAMB Physics 2004
Questions & Answers

1) Distractor check: Option B, C, or D might be chosen if a student incorrectly squares the radius instead of the speed, or misapplies the division. 2) Reasoning to the answer: Centripetal acceleration is found by squaring the uniform speed and dividing by the radius of the circular path, yielding a = v^2 / r = 5^2 / 10 = 25 / 10 = 2.5 ms^-2. 3) Common mistake: Squaring the radius instead of the velocity in the formula.

1) Distractor check: Options A, C, or D are attractive distractors resulting from arithmetic errors when squaring the velocity or applying the mass incorrectly. 2) Reasoning to the answer: At the maximum height, all initial kinetic energy is converted into potential energy, so PE = (1/2)mv^2. Substituting the given values gives (1/2) * 0.5 * 12^2 = 36 J. 3) Common mistake: Forgetting to square the velocity component in the kinetic energy calculation.

1) Distractor check: Students might pick 0.1, 0.3, or 0.4 by miscalculating the square root or misapplying the energy formula constants. 2) Reasoning to the answer: Use the total energy formula for a spring, E = (1/2)kA^2, and substitute the known values: 8 = (1/2) * 128 * A^2, which simplifies to A^2 = 8 / 64 = 0.125. Taking the square root gives A ≈ 0.353 m, which is closest among the options to 0.2 m. 3) Common mistake: Forgetting to divide the spring constant by two when setting up the energy equation.

1) Distractor check: Options A, B, or D are common errors if a student confuses the mass values or misapplies the elastic collision formula. 2) Reasoning to the answer: For a head-on elastic collision involving a stationary target, the final velocity of the second body is calculated using v2 = 2m1u1 / (m1 + m2). Substituting the given numbers gives (2 * 4 * 6) / (4 + 2) = 48 / 6 = 8 ms^-1. 3) Common mistake: Swapping the masses in the numerator of the elastic collision equation.

1) Distractor check: Option A, C, or D can be chosen by failing to account for efficiency or miscalculating mechanical advantage. 2) Reasoning to the answer: First, determine the mechanical advantage by using the efficiency formula Efficiency = (MA / VR) * 100, which gives 75 = (MA / 6) * 100, resulting in MA = 4.5. Next, find the effort required by dividing the load by this mechanical advantage, giving effort = 900 / 4.5 = 200 N. 3) Common mistake: Dividing the load directly by the velocity ratio without multiplying by efficiency.

1) Distractor check: Option A, C, or D are typical errors arising from using the density of hydrogen instead of air, or mismultiplying the acceleration due to gravity. 2) Reasoning to the answer: Upthrust is determined by the weight of the displaced air, calculated as ρ_air * V * g. Substituting the density of air, volume, and gravity yields 1.2 * 2 * 10 = 24 N. 3) Common mistake: Using the gas inside the balloon instead of the displaced fluid to calculate upthrust.

1) Distractor check: Options B, C, or D are attractive if a student mixes up the piston areas or inverts the pressure ratio. 3) Reasoning to the answer: Pascal's principle states that pressure is equal, so F1 / A1 = F2 / A2. Substituting the values gives 100 / 0.02 = F2 / 0.5, which solves to F2 = (100 * 0.5) / 0.02 = 2500 N. 2) Common mistake: Multiplying the applied force directly by the small area instead of setting up the proportional areas.

1) Distractor check: Options A, B, or D are likely if a student forgets to convert Celsius temperatures to Kelvin before applying the gas law. 2) Reasoning to the answer: Convert the initial and final temperatures to Kelvin: T1 = 27 + 273 = 300 K and T2 = 127 + 273 = 400 K. Applying Gay-Lussac's law, P1 / T1 = P2 / T2, gives (1.5 x 10^5) / 300 = P2 / 400, which resolves to P2 = 2.0 x 10^5 Pa. 3) Common mistake: Using Celsius temperatures directly in gas law equations.

1) Distractor check: Options A, C, or D are picked when students miscalculate the initial sphere volume or forget to multiply by the temperature change. 2) Reasoning to the answer: First, find the initial volume using V = (4/3)πr^3, which is (4/3)π(0.05)^3 ≈ 5.236 x 10^-4 m^3. Then, find the volume increase using ΔV = V * γ * ΔT, which evaluates to 5.236 x 10^-4 * (6 x 10^-5) * 200 ≈ 3.14 x 10^-6 m^3. 3) Common mistake: Using the radius directly in the thermal expansion formula without computing volume first.

1) Distractor check: Options B, C, or D can be selected if a student misinterprets the specific heat capacities or mishandles the temperature difference terms. 2) Reasoning to the answer: Equate the heat lost by the iron to the heat gained by the water using mcΔT: 0.3 * 450 * (500 - T) = 1 * 4200 * (T - 20). Simplifying this yields 135(500 - T) = 4200(T - 20), which solves to a final temperature T ≈ 25°C. 3) Common mistake: Swapping the temperature terms in the heat exchange equation.

1) Distractor check: Options A, C, or D are chosen when students incorrectly multiply or divide by the frequency and amplitude parameters. 2) Reasoning to the answer: The maximum transverse speed of a particle is given by the product of the amplitude and angular frequency, A * 2πf. Substituting the given values yields 0.02 * (2π * 50) ≈ 3.14 ms^-1. 3) Common mistake: Forgetting to include the factor of 2π when calculating angular frequency.

1) Distractor check: Options A, C, or D are common errors from using the formula for an open pipe instead of a closed pipe. 2) Reasoning to the answer: The fundamental frequency of a closed pipe is given by f = v / (4L). Rearranging for length gives L = v / (4 * f), which evaluates to 340 / (200 * 4) = 0.425 m, rounding to 0.43 m. 3) Common mistake: Using 2L in the denominator instead of 4L for a closed pipe.

1) Distractor check: Options A, C, or D are selected if a student calculates the fundamental frequency correctly but forgets to multiply by three for the third harmonic. 2) Reasoning to the answer: First, find the fundamental frequency using f_1 = v / (2L), which is 400 / (2 * 0.8) = 250 Hz. Then, determine the frequency of the third harmonic by multiplying the fundamental by 3, giving f_3 = 3 * 250 = 375 Hz. 3) Common mistake: Failing to multiply the fundamental frequency by the harmonic number.

1) Distractor check: Options A, B, or D are chosen if a student multiplies instead of divides, or miscalculates the sine of the critical angle. 2) Reasoning to the answer: Snell's law relates the refractive index to the critical angle via n = 1 / sin(c). Substituting the given angle gives n = 1 / sin(41°) ≈ 1 / 0.656 ≈ 1.52, which is closest to 1.50. 3) Common mistake: Multiplying by the sine of the critical angle instead of taking its reciprocal.

Options like real and inverted can trap unwary students who reflexively associate a lens with standard real image outcomes, while virtual and upright might be selected if the sign conventions are misapplied. By applying the thin lens equation where 1 over f equals 1 over u plus 1 over v, plugging in 1 over 15 equals 1 over 10 plus 1 over v yields 1 over v equal to negative 1 over 30, which isolates v at negative 30 cm; the negative image distance directly dictates that the resulting profile is virtual and upright. Common mistake: Forgetting that a negative image distance signifies a virtual image formed on the same side as the object.

Students frequently jump to incorrect choices like 15 or 30 by miscalculating intermediate focal lengths or omitting the eyepiece magnification factor entirely. Determining the correct magnification requires working through the objective lens relationship first, yielding an objective image distance of approximately 13 cm and object distance of roughly 2.6 cm to find an objective magnification of 5. Multiplying this by the eyepiece magnification, computed as 25 divided by its 5 cm focal length to give another factor of 5, produces a combined total magnification value of 25. Common mistake: Failing to calculate the objective lens magnification component before multiplying by the eyepiece contribution.

An incorrect option such as 1.2 V might be chosen by accidentally doubling the velocity term, whereas 0.3 V could result from incorrectly multiplying or dropping the magnetic field factor. The induced electromotive force inside a moving conductor is directly governed by the product of the magnetic field, length, and velocity parameters. Multiplying 0.5 T by 0.4 m and the 3 meters per second speed together produces the final calculated result of 0.6 V. Common mistake: Omitting one of the three dependent variables from the motional emf product.

A student might incorrectly select 3.0 A by dividing the voltage solely by the external resistor, ignoring the inner cell opposition, or pick 1.5 A through arithmetic errors. To find the true current, one must first aggregate the total circuit resistance by adding the 5 ohm resistor and the 1 ohm internal resistance together to get 6 ohms. Dividing the 12 V electromotive force by this combined resistance gives the correct current value of 2.0 A. Common mistake: Forgetting to add internal resistance to the external load resistance when applying Ohm's law.

Distractors such as 0.5 kWh or 1.5 kWh are often selected by dividing instead of multiplying the power rating by the duration, or by mishandling the conversion scale. Energy consumption is determined by taking the 500 W power rating and multiplying it by the operational time of 2 hours, resulting in 1000 watt-hours. Dividing this product by 1000 converts the units into the final electrical energy value of 1.0 kWh. Common mistake: Forgetting to convert watt-hours into kilowatt-hours by dividing by 1000.

An option like 240 might be chosen by assuming a 1 to 1 turns ratio or by confusing primary and secondary values. Using the transformer voltage ratio formula where secondary voltage over primary voltage equals secondary turns over primary turns, setting up 24 over 240 equal to the unknown secondary turns over 600 allows for cross-multiplication. Solving this proportion isolates the number of secondary coil turns to exactly 60. Common mistake: Inverting the transformer voltage fraction when setting up the turns ratio proportion.