WAEC Physics 2020 Theory Past Questions

Model answer

Given: Original length l0=3m, extension e=3l0=3x3=9m. Force constant k=982.3 Nm^-1. Correlating equation: F=ke. F=982.3x9=8840.7 N.

Model answer

(a) Function of metal plate of solar panel: Receives and absorbs solar radiation to produce heat. (b) Thermal insulator: Minimizes heat loss to the environment. (c) Tubes of solar panel: Helps in circulating the heat.

Model answer

(a) The material most suitable for the design of the core is pure glass (SiO2), plastic, or both. (b) To confine signal to the core of an optical fibre, the refractive index of the core must be greater than that of the cladding.

Model answer

Given: v is proportional to T^x mu^y, where T=Tension in the spring, mu=mass per unit length, v=velocity of a wave. Thus v=kT^x mu^y, where k is a dimensionless constant. Dimensionally: T(N)=kgm/s^2, T(N)=MLT^-2; mu=kgm^-1, mu=ML^-1. Thus, LT^-1=k[MLT^-2]^x[ML^-1]^y. LT^-1=k[m^x L^x T^-2x][M^y L^-y]. LT^-1=kM^(x+y)L^(x-y)T^-2x. Comparing the L.H.S and R.H.S terms: For M: x+y=0 (1). For L: x-y=1 (2). And for T: -1=-2x, x=1/2, and from (1): x+y=0, y=-1/2. Thus, v=kT^(1/2)mu^(-1/2), or v=k*sqrt(T/mu).

Model answer

Given: Escape velocity VE, radius of the earth=R. To show that VE=sqrt(2gR). Analysis: When the satellite just escapes the earth's gravitational attraction, the Gravitational potential energy equals the kinetic energy of the satellite, i.e. P.E.=K.E. GmM/R = (1/2)mVE^2. GM/R = (1/2)VE^2. VE^2=2GM/R. But GM=gR^2 (from g=GM/R^2). VE^2=2gR^2/R=2gR. Therefore, VE=sqrt(2gR).

Model answer

Given: theta=30 deg, T=25s, g=10m/s^2, required v=? Recall that Time of flight T=2usin(theta)/g. 25=2usin30/10. 250=2u(1/2). 250=u. Therefore, u=250 ms^-1.

Model answer

Properties of laser beams that make them preferable to ordinary light beams (any three): i. It is monochromatic i.e. having only one colour. ii. It gives more intense light/power. iii. It has a very narrow optical bandwidth. iv. It can be emitted continuously. v. It travels a very long distance without losing its intensity.

Model answer

(a)(i) A torque is defined as the turning effect of force about a pivot or an axis. (ii) Factors that determine a torque: Perpendicular distance of the force from its line of action to the pivot; Direction of the force; Magnitude of the force. (b)(i) A free fall is defined as the vertical motion of a body under the influence of acceleration due to gravity, or its own weight. (ii) Given u=10m/s, height of tower=40m. Using H=ut+(1/2)gt^2, taking downward as positive from the top of the tower and the body thrown upward first: -40=10t-(1/2)(10)t^2. -40=10t-5t^2. 5t^2-10t-40=0. Divide through by 5: t^2-2t-8=0. t^2-4t+2t-8=0. t(t-4)+2(t-4)=0. (t+2)(t-4)=0. t=-2 or t=4. Since time cannot be negative, t=4 s. (c) Given: Mass of wood = mass of water displaced + mass of oil displaced. Mass of wood = (rho.V)oil + (rho.V)water, where rho_oil = density of oil = 0.72x1000=720 gcm^-3(kg/m3 equivalent), rho_water = density of water = 1x1000=1000 gcm^-3. With V_oil = volume of oil displaced = volume of portion of wood in oil = lbh = 8x8x6cm^3=384cm^3=384x10^-6 m^3. Similarly, V_water = volume of water displaced = volume of portion of wood inside water = lbh(l=b=8cm, h=2cm)=128cm^3=128x10^-6 m^3. Thus, mass of wood = [720x384+1000x128]x10^-6 = [276,480+128,000]x10^-6 = [404,480]x10^-6 = 0.404 kg.

Model answer

(a)(i) Resonance frequency as applied to RLC series circuit: It is the frequency of oscillation of an RLC series circuit when the capacitive reactance Xc is equal to the inductive reactance XL and the impedance Z is equal to the resistance with the current maximum and the impedance minimum. (ii) [Sketch: graph of reactance (y-axis) against frequency (x-axis), showing XL as an increasing line and Xc as a decreasing curve, intersecting at the resonance frequency fo.] (iii) Relationship between current and voltage: (alpha) When f=fo, current is in phase with the supply voltage. (beta) When f less than fo, current leads the supply voltage. (gamma) When f greater than fo, current lags the supply voltage. (b)(i) Mutual inductance is defined as the ratio of the induced e.m.f. in one coil or circuit to the time rate of change of current in the other coil. It is also defined as the production of e.m.f. in a circuit as a result of the change in the magnetic flux in an adjacent circuit linked to it. (ii) Given: Number of turns N=500 turns, diameter d=8.0cm=8x10^-2m, B=0.25T, V=480V, pi=3.142. Correlating equation: Rotational induced e.m.f of an electric generator, E.m.f.=(omega)BAN. 480=omega x 0.25 x (pi d^2/4) x 500. 480=omega x 0.25 x [(8x10^-2)^2 x pi/4] x 500. 480=6284x10^-4 (omega). omega=480/0.6284=763.84 rad/s. (c)(i) Eddy current: These are currents induced and flows within a metal block when there is a change in magnetic flux linking the block. OR They are loops of electrical current induced within conductors by changing magnetic field in the conductor. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. (ii) Practical uses of Eddy currents: Induction heating furnaces to heat objects; Automobile speedometers; Induction alternating current (AC) motors; Induction coils.

Model answer

(a)(i) Critical angle is defined as the angle of incidence in the optically denser medium for which the angle of refraction in the less dense medium is 90 deg. i=c=critical angle when r=refracted angle=90 deg. (ii) Conditions necessary for total internal reflection to occur: light rays must travel from a denser medium to a less dense medium e.g. glass to air or glass to water or water to air; the angle of incidence in the denser medium must be greater than the critical angle (i>c). (iii) Practical applications of total internal reflection (TIR): Optical fibres used in the telecommunication field; Prism periscopes for viewing overhead objects; Prism Binoculars for viewing distance objects; Fish eye view; Transmission of radio signals. (b) Effects of refraction: Change in the direction of a wave; Change in the speed of a wave; Object appears raised when viewed above the water. (c)(i) A progressive wave is defined as a disturbance which travels through a medium that enables energy to be transferred from its source to another (without the particles of the medium being transferred). (ii) Given the wave equation y=0.5sin(1000(pi)t-100(pi)x/17): (alpha) To find the frequency of the wave, we recall the general equation of a progressive wave along the positive x-axis, i.e. y=Asin(omega*t - 2(pi)x/lambda) = Asin(2(pi)ft - 2(pi)x/lambda). Comparing this with the given equation, we have 2(pi)f=1000(pi), so f=1000(pi)/2(pi)=500 Hz. (beta) To find the wavelength of the wave, again we compare the two wave equations, i.e. 2(pi)x/lambda = 100(pi)x/17. So 2/lambda=100/17. lambda x 100 = 17x2. lambda=34/100=0.34 m. (gamma) To calculate the speed of the wave, using v=f*lambda: v=500x0.34, v is approximately 170 m/s.

Model answer

(a)(i) Mass of water evaporated = (New mass) - (Initial mass), calculated at each time interval from the balance readings: at 100s, mass evaporated=203.22-201.62=1.60g; at 200s, =203.22-199.79=3.43g; at 300s,=203.22-198.25=4.96g; at 400s,=203.22-196.50=6.72g. (ii) Energy supplied by heater = rate of energy supply x time = (38 J/s) x time. At 100s: 3800J; at 200s: 7600J; at 300s: 11,400J; at 400s: 15,200J (values filled based on the given rate of 38 J/s, consistent with the table's progression pattern of 0, 38.00, 76.00, 114.00, 152.00 in the units indicated in the table, i.e. in units of 10^2 J). (iii) I. Slope of the graph = (Delta Q)/(Delta m) = (Q2-Q1)/(m2-m1) = (11.2-2.0)x10^3 / (5.0-0.9) = 9.2x10^3/4.1 = 2.24x10^3 J/g. II. Meaning of the value of the slope of a graph: The slope = 2.24x10^3 J of heat is needed to evaporate 1 g of water at constant temperature; this represents the specific latent heat of vaporization of water. (b)(i) Saturated vapour pressure: The process of evaporation in a closed container will proceed until there are as many molecules returning to liquid as there are escaping. At this point, the vapour is said to be saturated. This is called the saturated vapour pressure of the liquid at that temperature. (ii) Factor affecting saturated vapour pressure: Temperature. Vapour pressure increases as the temperature increases and vice-versa.

Model answer

(a)(i) Isotopes are atoms of the same element with the same number of protons (atomic number) but different number of neutrons (mass number). (ii) Uses of radioactive tracers in medicine: Monitoring the function of the thyroid gland and other organs; Detection of blood clots in the brain; Diagnosis and treatment of disease; Sterilization of medical equipment. Uses of tracers in industry: Leakages in underground pipes; Wear and tear of machinery; Environmental pollution. Uses of tracers in agriculture: Determination of plants absorption of mineral elements; Study of the mechanism of photosynthesis; Seed preservation; Sterilization of insects; Food preservation. (b) Given: f=5.4x10^14 Hz, Emax=1.2x10^-19 J, required fo=? Using Emax=hf-Wo, E=hf-hfo=h(f-fo), so fo=f-(1.2x10^-19)/(6.6x10^-34)=5.4x10^14-0.1818x10^15=5.4x10^14-1.188x10^14=3.6x10^14 Hz. (c) Features common to electromagnetic waves: They are transverse waves; travel with the speed of light in vacuum; undergo refraction, reflection, diffraction, polarization and interference; travel through vacuum. (d)(i) Components of the nucleus reaction/nuclear reactor: Uranium fuel; Graphite moderator; Boron/Control rod; Coolant; Heat exchanger; Shield. (ii) Functions of the components of the nuclear reactor: Uranium rods - serves as fuel for the nuclear reaction; Graphite moderator - controls neutron population; Coolant - reduces the excessive heat produced in the nuclear reactor; Heat exchanger - converts the heat energy produced to other forms; Shield - to protect the operator and surrounding against extraneous radiations.