WAEC Physics 2022 Theory Past Questions

Model answer

Given: Time of flight, T=40s, u=250m/s, θ=42° (angle of projection). Distance |PQ| = range of projection = uₓT, where uₓ=u cosθ. |PQ| = u cosθ × T = 250 cos42° × 40 = 7431 m.

Model answer

Properties of an intrinsic semiconductor: - They are tetravalent, i.e. they have four valence electrons (Group IV elements). - They have thermally generated charge carriers. - They have an equal number of charge carriers, i.e. number of holes = number of electrons. - They are pure, i.e. they contain no impurities. - They have low electrical conductivity.

Model answer

E = K²/(m₁r²) = Gm₁m₂/r To find the dimensions of K, insert the respective dimensions of G and m: k² = M·L³T⁻²×M×M×L k² = M²L⁴T⁻² Multiply the powers on both sides of the equation by ½: k = M²L⁴T⁻²^(1/2) = ML²T⁻¹ Therefore, dimension of angular momentum = ML²T⁻¹.

Model answer

To find the workdone (w) by the force to stretch the string: Recall w = ½ke², with F=ke, e=F/k. So, w = ½ × k × (F/k)² = ½ × F²/k w = ½ × 50²/100 = ½ × 2500/100 = 12.5 J.

Model answer

(a) A geostationary satellite is an artificial satellite whose period of revolution is equal to the period of rotation of the Earth (24 hours/1 day). It is a satellite whose period of revolution is equal to the period of rotation of the Earth about its own axis. (b) Types of LASERS: - Solid state - Liquid - Gas - Semi-conductor (LASER diodes) - Chemical - Fibre Note: LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. It is a device that stimulates atoms or molecules to emit light at particular wavelengths and amplifies that light, typically producing a very narrow beam of radiation.

Model answer

(a) The S.I. unit of the intensity of a blackbody radiation is Wm⁻² or Js⁻¹m⁻². The intensity I(λ,T) of blackbody radiation depends on the wavelength λ of the emitted radiation and the temperature of the blackbody. It is the power radiated per unit area. Radiation emitted by materials approximately follows the blackbody radiation curve. (b) Features of the intensity-wavelength graph of a perfect blackbody at different temperatures: - Shape of the curve is non-symmetric. - The line joining the peaks has a negative gradient. - Peaks decrease with wavelength. - Each curve corresponds to a different blackbody temperature, starting from a low temperature (lowest) curve to a high temperature (highest) curve.

Model answer

Magnetic materials | Non-magnetic materials - They are attracted to/by magnets. | They are not attracted to/by magnets. - The magnetic domains of the magnetic fields align themselves in an orderly fashion. | The domains of the magnetic fields are randomly aligned. - They can be magnetized. | They cannot be magnetized.

Model answer

(a)(i) The law of inertia states that a body continues in its state of rest or uniform linear motion unless acted upon by an external force to act otherwise. (ii) How a safety belt works using the law of inertia: The safety belt acts as an external force which prevents a passenger from an otherwise forward motion after impact or collision (the passenger's body, by inertia, would continue moving forward when the vehicle suddenly stops, and the belt provides the restraining force). (b)(i) Moment of force is defined as the product of a force and perpendicular distance from a reference point or pivot to the line of action of the force. (ii) I. [Force diagram: plank AB, 2m long, with W=54N acting at midpoint (1m from A), knife edge (reaction R) at 0.5m from B (i.e. 1.5m from A), and tension T acting vertically upward at A.] II. Taking moments about the knife edge: T×1.5 = 54×0.5 (sum of clockwise moment = sum of anticlockwise moment about the pivot)... [T=18N per similar worked example] III. At equilibrium, ΣF=0: T+R=54, so R=54−T=54−18=36N. (c) Differences between solid friction and viscosity: Solid friction | Viscosity - Occurs on solid surfaces | Occurs in fluids (liquid and gas) - Independent of area of surfaces in contact | Depends on area of the surface in contact - Depends on the nature of the surfaces in contact | Depends on the speed of motion between the layers of the fluid - Independent of temperature | Depends on temperature (d) Method of increasing the velocity ratio of a pulley system: By increasing the number of pulleys used in the system.

Model answer

(a)(i) Coulomb's law of electrostatics states that the electrostatic force between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. (ii) Given: r=5.2×10⁻¹¹m, e=q=1.6×10⁻¹⁹C, k=(4πε₀)⁻¹=9×10⁹mF⁻¹ Using F=kq₁q₂/r²: F = (9×10⁹×1.6×10⁻¹⁹×1.6×10⁻¹⁹)/(5.2×10⁻¹¹)² F = 23.04×10⁻²⁹/27.04×10⁻²² F = 8.52×10⁻⁸N. (b)(i) Let the current through the circuit be I. Vᵢₙ=I(R₁+R₂) ...(1) Vₒᵤₜ=IR₂ ...(2) Dividing (2) by (1): Vₒᵤₜ/Vᵢₙ = R₂/(R₁+R₂) Therefore, Vₒᵤₜ=Vᵢₙ(R₂/(R₁+R₂)). (ii) Given Vᵢₙ/Vₒᵤₜ=2.5, R₁=30Ω. Inverting the equation: Vᵢₙ/Vₒᵤₜ=(R₁+R₂)/R₂ ⟹ 2.5=(30+R₂)/R₂ ⟹ 2.5R₂=30+R₂ ⟹ 1.5R₂=30 ⟹ R₂=20Ω.

Model answer

(a)(ii) The volt is defined as the potential difference between two points in a conductor when one joule of work is done in moving one coulomb of charge (electricity) between the two points. (c) Wood is not suitable for use as the core of transformers because it is not a magnetic material and this would not provide magnetic coupling between coils for electromagnetic induction. The main purpose of using a core in a transformer is to carry the flux; magnetic materials (e.g. iron/steel) are used in transformer cores because of their tendency to carry or link the flux in the primary and secondary windings. A wooden core cannot provide this linkage. (d) Applications of cathode ray tube: For studying alternating current wave form; for measuring frequency/voltage/reactance/power factor and resistance of an electronic device; used to monitor signals/check FM/AM characteristics.

Model answer

(a)(i) Conditions for constructive interference of waves: It must involve at least two waves; waves must vibrate in phase; the distance between the sources of the wave must be of the order of the wavelength. (ii) Conditions for total internal reflection: The waves must travel from a denser medium to a less dense medium; the angle of incidence (in the denser medium) must be greater than the critical angle. (iii) Conditions for production of beats: The amplitude of the two interfering waves should be the same; the difference between the frequencies of interfering waves should be small; the two sources of waves must be sounded together. (b) Calculation of velocity of sound in air: l₁=35cm, l₂=100cm are lengths of air column for two consecutive resonance positions when tuning fork of frequency f is sounded. l₂−l₁=λ/2, so λ=2(l₂−l₁)=2(100−35)−(end correction adjustments)=2×65=130cm (approx, per standard resonance tube method, adjusting for end correction) v=fλ=2×256×(100−0.35)=... per source's detailed calculation, v=332.80m/s. (c)(i) Three classifications of musical instruments: Wind; Stringed; Percussion. (ii) Examples: wind — flute, trumpet, pipe, organ; stringed — piano, guitar, violin; percussion — drum, bell, gong, xylophone. (d) Calculation of critical angle: n=1/sinC. 1.5=1/sinC. sinC=0.6667. C=sin⁻¹0.6667=41.80°. (e) Using v∝√T (speed of sound proportional to square root of absolute temperature): V₁/√T₁=V₂/√T₂. T₁=102+273=375K, V₁=240m/s, V₂=310m/s. √T₂=(310×√375)/240=25.0067. T₂=625.3K.

Model answer

(a)(i) Artificial radioactivity is the process by which a stable nucleus is bombarded with a neutron to make it unstable and so disintegrates/decays with the emission of particles/radiations and energy. (ii) Completed table: Emission | Nature | Charge | Ionizing ability Beta | High speed electron | Negative | Moderately ionizing Gamma | Electromagnetic radiation | Neutral | Negligible Alpha | Helium nucleus | Positive | High ionizing (b) K.E of electron = eV K.E = 1.6×10⁻¹⁹ × 30×10³ K.E = 4.8×10⁻¹⁵J.