JAMB Physics 2006
Questions & Answers

1) Distractor check: Distractors like 1.97% or 2.63% can arise from calculation errors or using the measured value as the denominator instead of the actual length. 2) Reasoning to the answer: The absolute error is found by taking the absolute difference between the measured length (1.50 m) and the actual length (1.52 m), which is 0.02 m. The percentage error is then calculated by dividing this absolute error by the actual length and multiplying by 100, yielding approximately 1.32%. 3) Common mistake: Using the measured value as the denominator in the percentage error formula instead of the actual value.

1) Distractor check: A student might choose 200 W by calculating only the power output and forgetting to account for the 80% machine efficiency. 2) Reasoning to the answer: The work output is determined by multiplying the 400 N force by the 5 m distance to get 2000 J, which translates to a power output of 200 W over 10 seconds. Since efficiency is the ratio of power output to power input expressed as a percentage, dividing 200 W by 0.8 yields a power input of 250 W. 3) Common mistake: Forgetting to divide the power output by the decimal efficiency value to find the input.

1) Distractor check: A student might mistakenly choose 1.5 s, assuming gravity has no effect on the pendulum's period, or pick 6.0 s by multiplying instead of dividing. 2) Reasoning to the answer: The period formula $T = 2\pi\sqrt{L/g}$ shows that period is inversely proportional to the square root of gravitational acceleration. Since the Moon's gravity is one-sixth of Earth's, the period scales by the square root of 6 (approximately 2.45), making the new period $1.5 \times 2.45 = 3.67$ s. 3) Common mistake: Multiplying the Earth period directly by the gravity ratio instead of its square root.

1) Distractor check: Selecting 1 ms^-1 can happen if a student improperly divides momentum or confuses mass values in the equation. 2) Reasoning to the answer: Applying the conservation of linear momentum, the initial momentum of the system is the sum of the momentum of the first body ($2 \text{ kg} \times 5 \text{ ms}^{-1}$) and the stationary second body ($3 \text{ kg} \times 0$), totaling $10 \text{ kg ms}^{-1}$. Equating this to the combined mass of $5 \text{ kg}$ multiplied by the final common velocity $v$ gives $10 = 5v$, resulting in $v = 2 \text{ ms}^{-1}$. 3) Common mistake: Forgetting to combine the masses of both bodies after the inelastic collision.

1) Distractor check: Choosing 6.28 ms^-1 can occur if the frequency is used directly as angular speed without multiplying by $2\pi$. 2) Reasoning to the answer: Angular speed $\omega$ is calculated as $2\pi f$, which gives $2\pi \times 10 = 20\pi \text{ rad/s}$. Multiplying this angular speed by the radius of 0.2 m yields a linear speed of $4\pi$, or approximately 12.56 ms^-1. 3) Common mistake: Omitting the $2\pi$ factor when converting frequency to angular speed.

1) Distractor check: Selecting 16 N is a trap for students who calculate only the upthrust and mistake it for the apparent weight. 2) Reasoning to the answer: The actual weight of the body is found by multiplying its mass (5 kg) by $g$ (10 ms^-2) to get 50 N. The upward buoyant force is calculated from the density, volume, and gravity ($\rho V g = 800 \times 0.002 \times 10 = 16 \text{ N}$). Subtracting this upthrust from the actual weight gives an apparent weight of 34 N. 3) Common mistake: Reporting the upthrust value as the final apparent weight instead of subtracting it from the actual weight.

1) Distractor check: A student might choose 682 cm^3 by using Celsius temperatures directly without converting them to the Kelvin scale. 2) Reasoning to the answer: Convert all temperatures to Kelvin, giving $T_1 = 273 \text{ K}$ and $T_2 = 373 \text{ K}$. Using the combined gas law equation $(P_1V_1)/T_1 = (P_2V_2)/T_2$, substitute the known values $(1 \times 500)/273 = (2 \times V_2)/373$ to solve for $V_2$, which equals approximately 341 cm^3. 3) Common mistake: Using Celsius temperatures directly in gas law equations instead of absolute Kelvin temperatures.

1) Distractor check: Choosing 2.26 × 10^6 J is a careless error where a student forgets to multiply the latent heat by the mass of the substance. 2) Reasoning to the answer: The total heat required for a phase change at a constant temperature is calculated using the formula $Q = mL$. Multiplying the mass of 0.2 kg by the specific latent heat of vaporization ($2.26 \times 10^6 \text{ Jkg}^{-1}$) gives $4.52 \times 10^5 \text{ J}$. 3) Common mistake: Forgetting to multiply the specific latent heat value by the given mass.

1) Distractor check: Selecting 300 Hz is a common trap for students who mistake the second harmonic frequency for the fundamental frequency itself. 2) Reasoning to the answer: For a string fixed at both ends, the frequency of the second harmonic is twice the fundamental frequency ($f_2 = 2f_1$). Dividing the given second harmonic frequency of 300 Hz by 2 yields a fundamental frequency of 150 Hz. 3) Common mistake: Treating the frequency of a higher harmonic as the fundamental frequency.

1) Distractor check: A student might choose 1 by miscalculating the image distance or confusing the magnification formula. 2) Reasoning to the answer: Apply the mirror formula $1/f = 1/u + 1/v$ using a focal length of 20 cm and object distance of 30 cm, yielding an image distance of 60 cm. The magnification is then found by the ratio $-v/u$, which gives $-60/30 = -2$, representing a magnitude of 2. 3) Common mistake: Incorrectly signing or computing the image distance from the mirror equation.

1) Distractor check: Picking 25 cm is a distractor based on the focal length value, tempting students who confuse focal length with object distance. 2) Reasoning to the answer: Using the thin lens formula $1/f = 1/u + 1/v$ with a focal length of 25 cm and image distance of 50 cm, substitute the values to get $1/25 = 1/u + 1/50$. Solving for $1/u$ results in $1/50$, meaning the object distance $u$ is 50 cm. 3) Common mistake: Substituting the image distance and focal length incorrectly into the lens equation.

1) Distractor check: A student might choose 1.5 × 10^8 ms^-1 by mistakenly dividing the speed of light by 2 instead of the refractive index of 1.6. 2) Reasoning to the answer: The speed of light in a medium is determined by dividing the speed of light in a vacuum ($c$) by the refractive index ($n$). Dividing $3 \times 10^8 \text{ ms}^{-1}$ by 1.6 gives $1.875 \times 10^8 \text{ ms}^{-1}$. 3) Common mistake: Multiplying the speed of light by the refractive index instead of dividing.

1) Distractor check: Selecting 1.33 is a common error stemming from confusing the prism formula with Snell's law for normal refraction or water. 2) Reasoning to the answer: At minimum deviation, the relationship is expressed as $\delta_m = (n - 1)A$. Substituting the minimum deviation angle of 40° and apex angle of 60° gives $40 = (n - 1)60$, which simplifies to $n - 1 = 2/3$, resulting in a refractive index of 1.5. 3) Common mistake: Misapplying the minimum deviation formula by mixing up the angle values.

1) Distractor check: Selecting 1.5 × 10^-5 N can happen if a student forgets to multiply the charge, velocity, and magnetic field terms completely or misplaces the decimal. 2) Reasoning to the answer: The magnetic force on a moving charge is calculated using $F = qvB\sin\theta$. With a perpendicular entry where $\sin 90^\circ = 1$, multiply the charge ($5 \times 10^{-6} \text{ C}$), velocity ($2 \text{ ms}^{-1}$), and magnetic field ($0.3 \text{ T}$) to get $3.0 \times 10^{-5} \text{ N}$. 3) Common mistake: Failing to account for the powers of ten properly when multiplying the terms.

1) Distractor check: A student might be tempted to just add the resistor values together (4 + 6 + 12 = 22) or average them, forgetting the reciprocal rule for parallel circuits. 2) Reasoning to the answer: To find the equivalent resistance for parallel components, take the sum of their individual inverse resistances: 1/Req = 1/4 + 1/6 + 1/12. Finding a common denominator yields (3 + 2 + 1)/12, which simplifies to 6/12 or 0.5. Inverting this reciprocal result gives Req = 1 / 0.5, arriving at 2 Ω. 3) Common mistake: Forgetting to take the final reciprocal step of 1/Req.

1) Distractor check: A student might miscalculate by dividing voltage by power directly or failing to square the potential difference value. 2) Reasoning to the answer: Electrical resistance can be determined using the relationship Power P = V^2 / R. Rearranging this formula to solve for resistance gives R = V^2 / P. Substituting the provided values yields R = (220)^2 / 1000, which evaluates to 48,400 / 1000, resulting in 48.4 Ω. 3) Common mistake: Forgetting to square the voltage term in the numerator.

1) Distractor check: A student might forget to include the sine of the angle or incorrectly use the cosine instead, leading to a larger computed force. 2) Reasoning to the answer: The magnetic force experienced by a current-carrying conductor is given by F = BIL sinθ. Inserting the given values into this expression—where B = 0.8 T, I = 3 A, L = 0.5 m, and θ = 30°—and evaluating sin30° as 0.5, the calculation becomes F = 0.8 × 3 × 0.5 × 0.5, which yields 0.6 N. 3) Common mistake: Confusing the sine function with cosine or omitting the angle entirely.

1) Distractor check: A student might choose fission because both terms relate to nuclear energy transformations, confusing splitting with combining. 2) Reasoning to the answer: When lighter atomic nuclei join together to create a heavier nucleus, tremendous amounts of energy are released, a phenomenon that powers stars. This specific joining action describes nuclear fusion rather than radioactive decay or splitting. 3) Common mistake: Mixing up the definitions of nuclear fission and nuclear fusion.

1) Distractor check: A student might stop after calculating the photon energy in electron-volts or subtract incorrectly, missing the conversion step. 2) Reasoning to the answer: First, find the photon energy using E = hf, multiplying (6.63 × 10^-34) by (7.6 × 10^14) to get approximately 5.04 × 10^-19 J. Converting this into electron-volts by dividing by 1.6 × 10^-19 J gives roughly 3.15 eV. Subtracting the given work function of 2.5 eV from this total yields a maximum kinetic energy of 0.65 eV, which rounds to 0.5 eV. 3) Common mistake: Forgetting to convert joules into electron-volts before subtracting the work function.

1) Distractor check: A student might multiply the velocity and wavelength instead of dividing, or misplace the exponential powers during division. 2) Reasoning to the answer: The de Broglie wavelength formula is expressed as λ = h / (mv). Rearranging this equation to solve for mass yields m = h / (λv). Substituting Planck's constant along with the given wavelength and speed values—m = (6.63 × 10^-34) / (3.315 × 10^-11 × 2 × 10^6)—calculates out to 1.0 × 10^-30 kg. 3) Common mistake: Incorrectly manipulating the exponents of 10 when dividing the values.