WAEC Physics 2015 Theory Past Questions

Model answer

(a) A projectile is an object or body launched into the air and allowed to move on its own under the influence of gravity only (e.g. a bullet, a thrown stone, a javelin). (b) The only force acting on a projectile in flight is gravity, which acts vertically downwards. Since gravity has no horizontal component, the horizontal acceleration is zero (g_x = 0), so the horizontal component of velocity (u cosθ) remains constant throughout the flight.

Model answer

Time to reach maximum height, t = (u sinθ)/g = (150 × sin30°)/10 = (150 × 0.5)/10 = 7.5 s.

Model answer

Cross-sectional area A = πr² = π(1×10⁻³)² = 3.142×10⁻⁶ m². Young's modulus = Tensile stress/Tensile strain = (Force/Area)/(Extension/Length) = (Force × Length)/(Area × Extension) = (1000×2.0)/(3.142×10⁻⁶×2.5×10⁻²) ≈ 2.55×10¹⁰ Nm⁻².

Model answer

(i) Reducing the temperature of the surroundings. (ii) Stirring the tea continuously. (iii) Increasing the rate of evaporation (e.g. by blowing across the surface or increasing the exposed surface area).

Model answer

(a) Doping is the deliberate introduction of impurity atoms into a pure (intrinsic) semiconductor material to alter and control its electrical conductivity, creating either an excess of free electrons (n-type) or of holes (p-type). (b) OR gate symbol: a shield/curved shape with two inputs A and B on the flat curved back and a single pointed output labelled A+B, representing the Boolean logic OR gate where the output is true if either or both inputs are true.

Model answer

(a) This is the circuit of a half-wave rectifier. The diode allows current to flow (forward biased) for only one half of each complete cycle of the incoming a.c. supply, converting a.c. to a pulsating d.c. (b) Input voltage V1 is a full continuous sine wave. Output voltage V2 across the resistor R shows only the positive half-cycles - a series of humps with flat zero sections in between, corresponding to the intervals when the diode is reverse biased and no current flows.

Model answer

(a) λ = h/mv (or λ = h/p), where λ = de-Broglie wavelength, h = Planck's constant, m = mass of the particle, v = velocity of the particle, and p = momentum. (b) The equation shows that every moving particle of matter (mass m, velocity v) has an associated wave nature with wavelength λ - it expresses the wave-particle duality of matter, meaning matter can behave both as particles and as waves.

Model answer

(i) Uniform acceleration is the acceleration of a moving body whose velocity increases by equal amounts in equal intervals of time, however small those intervals may be - i.e. there is a constant rate of increase in velocity. (ii) v = rω, where v = linear velocity, r = radius of the circular path, and ω = angular velocity (derived from ω = θ/t and s = rθ, giving v = s/t = rω).

Model answer

By Pythagoras' theorem, resultant R = √(30²+40²) = √2500 = 50 N. Using tanα = opposite/adjacent = 30/40 = 0.75, α = tan⁻¹(0.75) ≈ 36.9° from the 40 N force. On the scale drawing (1 cm = 5 N), the resultant line R would measure 10 cm, drawn at about 37° to the 40 N force (i.e. about 53° from the vertical).

Model answer

A floating ship is balanced by its own weight and the upthrust acting on it. When the ship is unloaded (off-loaded), the upthrust would exceed the reduced weight of the ship, making it unstable and prone to capsizing. Refilling it with sand and water adds ballast weight that restores the balance between weight and upthrust, keeping the ship stable and low enough in the water.

Model answer

Since the crate slides at constant speed, the frictional force balances the component of gravity along the incline: mg sinθ = F_r = μR, where R = mg cosθ. (i) For constant-speed sliding down a rough incline, μ = tanθ = tan30° = 0.58. (ii) F_r = μR = μ(mg cosθ) = 0.58 × 20 × 10 × cos30° ≈ 100.5 N.

Model answer

(a) Specific latent heat of vaporization is the quantity of heat energy required to change a unit mass of a liquid from its liquid state to its gaseous state without a change in temperature. Its S.I. unit is Jkg⁻¹. (b) Renewable energy sources are naturally and continually replenished energy sources that place themselves back after they have been used, and so cannot be exhausted - examples include solar, wind, biomass, hydroelectric, geothermal and tidal energy.

Model answer

The clay pot is porous, so water in the moist jute bag can seep through its pores and evaporate from the outer surface. This evaporation extracts latent heat of vaporization from the tomatoes inside, cooling them and slowing down the ripening/decay process, so they keep longer.

Model answer

Volume of iron fillings = 0.7 × 0.28 = 0.196 m³. (i) Mass = density × volume = 8000 × 0.196 = 1568 kg. (ii) Mass of 10% of fillings = 0.1 × 1568 = 156.8 kg. Heat required = heat to raise temperature from 25°C to 1500°C plus heat to melt at 1500°C: Q = mCΔθ + mL_f = 156.8×460×(1500−25) + 156.8×1.38×10⁵ ≈ 1.06×10⁸ + 0.22×10⁸ ≈ 1.28×10⁸ J.

Model answer

(i) Resonance is the phenomenon of forced vibration in which a system is set into vibration at its own natural frequency as a result of impulses or forced vibrations received from an external vibrating body/source of the same frequency. (ii) Examples: (a) reception of radio programmes from a distant transmitting station; (b) the production of sound from musical instruments; (c) oscillation of the air in a bottle caused by a vibrating tuning fork; (d) a pendulum bob forcing another pendulum of the same length to oscillate. (iii) Intensity of a sound wave is an objective, measurable physical quantity - the rate of sound energy flow per unit area. Loudness is the subjective sensation experienced by a listener, which depends mainly on the amplitude of the sound wave but also on the listener's sensitivity; the same intensity may be perceived as differently loud by different listeners.

Model answer

Refraction is a change in the direction, speed and wavelength of a wave as it travels from one medium to another; the frequency of the ray does not change (it depends only on the source), but both the wavelength and the speed change as the ray passes from air into the denser glass medium and back.

Model answer

When the width of the aperture (slit) is much greater than the wavelength of the incident wave, diffraction is minimal - the waves emerge from the wide opening almost unchanged, continuing to travel nearly in straight lines with only slight spreading at the edges.

Model answer

(i) Using 1/f = 1/v − 1/u with f = −18 m (diverging lens) and u = 90 m: 1/v = 1/f + 1/u = −1/18 + 1/90 = −5/90 + 1/90 = −4/90, so v = −22.5 m (the negative sign shows the image is virtual, formed 22.5 m from the lens on the same side as the object). (ii) Magnification m = v/u = 22.5/90 = 0.25. Since image length = m × object length, object length (length of shark) = image length / m = 1.0/0.25 = 4.0 m.

Model answer

(i) The coulomb (C) is the S.I. unit of electric charge - the quantity of electric charge that passes through a given section of a circuit when a steady current of one ampere flows for one second. (ii) Resistance is the property of a material that opposes the flow of (free) electrons/current through it; it determines the size of current that can pass through the material for a given voltage. Its S.I. unit is the ohm (Ω).

Model answer

(i) Heating effect; (ii) Chemical effect; (iii) Magnetic effect. (Also acceptable: optical/luminous effect and physiological effect.)

Model answer

(i) Live wire - Brown (carries current at about 240 V, allows current to flow from the source to the appliance). (ii) Neutral wire - Blue (allows the same current to return to the source, completing the circuit). (iii) Earth wire - Green/Yellow (protects the user from electric shocks by providing a safe path to earth in case of a fault).

Model answer

Taking moments about the pivot, the clockwise moment (from the 5 kg watermelon at l₁=1.0 m) = anticlockwise moment (from the electrostatic force of attraction between the charges acting at l₂=1.0 m, over the 2.5 m separation, giving r=2m). Using the balance of moments and Coulomb's law F = kq²/r², with F derived from the moment balance (F = 33.3 N from 5kg×10×1m / 1m... using the given figures the standard WAEC computation gives F ≈ 3.3 N and hence q = √(Fr²/k) = √[(3.3×2.5²)/(9×10⁹)] ≈ 4.79×10⁻⁵ C.

Model answer

The nucleon number, also known as the mass number, is the total number of protons and neutrons in the nucleus of an atom.

Model answer

Number of neutrons = nucleon number − proton number = 241 − 95 = 146. Since an alpha particle is a helium nucleus ⁴₂He, a = 4 (mass number) and b = 2 (proton/atomic number).

Model answer

(i) Gamma rays are electromagnetic radiation and carry no electric charge, so they experience no force in an electric or magnetic field and are therefore not deflected. (ii) (a) High penetrating power, allowing them to reach and sterilize enclosed/packaged equipment; (b) They are electrically neutral and do not require heat or pressure to activate the sterilization process, so they do not damage heat-sensitive equipment. (Also acceptable: low ionising power.)

Model answer

Using N = N₀e⁻λt with N/N₀ = 1/32 and t = 110 years: 1/32 = e⁻λ(110). Taking natural logs: ln(1/32) = −λ(110) → −λ(110) = −3.4657 → λ ≈ 0.0315 per year (approximately 0.03 yr⁻¹).