WAEC Physics 2011 Theory Past Questions

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A vector quantity is a physical quantity that has both magnitude and direction.

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Resolving into horizontal and vertical components: V1(3ms⁻¹, N45°W): horizontal = -3sin45° = -2.12, vertical = 3cos45° = 2.12. V2(12ms⁻¹, W): horizontal = -12, vertical = 0. V3(5ms⁻¹, S): horizontal = 0, vertical = -5. Sum: Vx = -14.12, Vy = -2.88. Resultant V = sqrt(Vx² + Vy²) = sqrt(14.12² + 2.88²) = sqrt(199.37+8.29) = sqrt(207.66) = 14.4 m/s. Direction: tanθ = 2.88/14.12 = 0.204, θ = 11.53°. Resultant v = 14.4m/s, W11.53°S (or S78.65°W).

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(i) Weight W(N) = mass(kg) x g: 0.5, 1.0, 1.5, 2.0, 2.5 N for masses 50g-250g respectively; extension e/m: 6.5x10⁻², 11.0x10⁻², 15.0x10⁻², 20.0x10⁻², 25.0x10⁻² m. (iii) Slope = ΔW/Δe = (W2-W1)/(e2-e1) = (2-0.65)/(20-6.5)x10⁻² = 1.35/13.5x10⁻² = 10 N/m. This slope is the force constant k = 10 N/m. (iv) Extension = final length - original length. When loaded with 250g, extension = 25cm and final length = 38.0cm. Natural (original) length = final length - extension = 38 - 25 = 13cm.

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Diffusion is the tendency of molecules to migrate to fill an empty space due to their random thermal or molecular motions. In diffusion, the molecules move from a region of high concentration to a region of low concentration.

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The rate of diffusion is higher in gases than in liquids because in gases there is more space for the molecules to move, and molecular motion is faster in gases due to weaker intermolecular forces compared with liquids.

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A plane polarized light vibrates in only one direction or plane (perpendicular to the direction of propagation), while an ordinary (unpolarized) light vibrates in different (all) directions.

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Uses of polaroid: (i) In sunglasses, to reduce the amount of light intensity entering the eye by reducing glare from wet surfaces (blocking some reflected light). (ii) In stress analysis or photo-elasticity. (iii) In the measurement of concentration of sugar solution (saccharimetry) (any two).

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(a) Applications of electrolysis in industry: (i) electroplating, (ii) extraction of metals (electrometallurgy), (iii) purification of metals such as copper, silver, gold, aluminium etc, (iv) manufacturing of non-metals such as hydrogen (any two). (b) Application in school laboratory: determination of equivalent mass of elements; manufacturing of compounds such as NaOH; electrolysis of acidified water; calibration of an ammeter (any one).

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Work done by force causing the shrink is given by W = ½kx² = ½ x 2.0x10^11 x (2x10⁻²)² = 4x10^7 J.

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Water molecules are more strongly attracted to glass molecules than to other water molecules. Thus, adhesive forces are stronger than cohesive forces, resulting in the rise of water level at the edge of a glass container/narrow tube, forming a concave meniscus. In mercury, the cohesion forces are stronger than the adhesive forces, so mercury forms a convex meniscus.

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Methods of polarizing an unpolarized light: (i) using Polaroid, (ii) polarization by reflection, (iii) polarization by double refraction, (iv) polarization by scattering, (v) polarization by selective absorption (any three).

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Energy of the electron, E = qV = 1.6x10⁻¹⁹ x 1x10^5 = 1.6x10⁻¹⁴ J.

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Properties of cathode rays suggesting particle nature: (i) possession of momentum, (ii) deflection in electric/magnetic fields (suggesting presence of charged tiny granules of matter), (iii) shadow formation (their path is blocked by objects in their path).

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The uncertainty principle is expressed by: Δx.Δp ≥ h or ΔE.Δt ≥ h, where h = h/2π = 1.054x10⁻³⁴ Js. Given Δt = 2x10⁻⁹s: ΔE ≥ h/Δt = 1.054x10⁻³⁴/(2x10⁻⁹) = 5.27x10⁻²⁶ J.

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A vector quantity is a physical quantity that has both magnitude and direction.

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See solution to Q1(b) above: horizontal components sum to -14.12, vertical components sum to -2.88.

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Resultant of the vectors V = sqrt(Vx²+Vy²) = sqrt((-14.12)²+(-2.88)²) = sqrt(199.37+8.29) = sqrt(207.66) = 14.4 m/s. Direction θ = tan⁻¹(2.88/14.12) = 11.53°, so v = 14.4m/s, W11.53°S or S78.65°W.

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(I) Alcohol has a lower freezing point of -114°C (mercury freezes at -38.8°C) and thus can be used for measuring very low temperatures. (II) Expansivity: the expansivity of alcohol is about six times that of mercury for the same temperature rise. (III) Alcohol is cheaper than mercury.

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This is because the glass of the bulb first expands (since it is in contact with the hot water first) and hence the mercury level falls. But the expansion of the mercury increases more than that of the glass, so at a point the mercury level rises.

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See worked solution in 12(c) below for the lead heating calculation.

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(i) Quantity of heat required to heat the lead to its melting point Q = mLCLΔT = 100x120x(320-40) = 3.36x10^6 J. (ii) Additional heat required to melt the lead = mLlf where lf = latent heat of fusion of lead. Qf = 100x2.5x10^4 = 2.5x10^6 J. (iii) Time taken to supply the additional heat: T = additional heat energy introduced / electric power = 2.5x10^6/10x10^3 = 250s.

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Precautions: (i) the calorimeter should be well lagged, (ii) the calorimeter should be shielded from the heat source, (iii) the mixture should be gently and continually stirred, (iv) dry steam should be used (any two).

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An eclipse is the partial or total blockage/obstruction of a planetary luminous body by another. It occurs when the sun, moon and earth lie in a straight line.

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Types of eclipse: solar eclipse, lunar eclipse, annular eclipse.

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The eye defect the student has is long sightedness (hypermetropia). The lens is unable to adjust itself to become thick enough for looking at close objects, so rays are not bent inwards enough to reach the retina before meeting.

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To correct long sightedness, a convex (converging) lens is used. It bends rays inwards a little before it enters the eye.

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Power of lens = 1/focal length. Where focal length = 10cm = 0.1m, Power of lens = 1/0.1 = 10D (dioptre).

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v = 2d/t, so d = vt/2. Given speed of sound v = 340 m/s, time t = 5.6x10⁻³s: d = (340 x 5.6x10⁻³)/2 = 0.952 m.

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Image distance v = -9cm (behind the mirror), magnification m = v/u = 0.6, so u = v/m = -9/0.6 = -15cm. Using 1/f = 1/u + 1/v: 1/f = 1/(-15) + 1/(-9) = -1/15 - 1/9 = -3/45-5/45 = -8/45? (Using magnitudes as per official solution): 1/f = 1/u - 1/v = 1/15 - 1/9 = (3-5)/45 = -2/45, therefore f = -22.5 cm.

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Mutual induction is a phenomenon whereby a conducting path (or circuit) with changing magnetic flux induces an e.m.f in another conducting path or in a nearby conducting path.

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Electromagnets are used in: (i) producing intense magnetic fields such as those required in generators and electric meters, (ii) lifting and transporting heavy pieces of iron and steel, plates, ladders, scrap iron etc, (iii) separating iron from mixtures containing non-magnetic substances, (iv) the operation of electromagnetic devices such as electric bell, telephone earpiece, magnetic relay and circuit breakers.

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(i) The lamp is lit when the a.c supply is switched on because the changing magnetic flux in X induces a corresponding changing magnetic flux in Y, which induces current that lights up the bulb. (ii) The brightness increases when the distance between X and Y decreases because as the distance decreases, the flux density linking coil Y increases, thus increasing the e.m.f/voltage induced in Y and consequently the brightness of the lamp. (iii) The filament of the lamp glows brighter when a bundle of insulated iron wires is placed along the common axis of the coils because the insulated soft iron wires concentrate/increase the magnetic flux through coil Y, thus increasing the e.m.f in Y, making the filament of the lamp glow brighter.

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(i) Circuit: two cells (V1=2.0V, r1=0.4Ω and V2=2.0V, r2=0.1Ω) connected in parallel, in series with a 5Ω resistor. (ii) Since both cells have the same emf (2V), the total voltage across the parallel combination = 2V. The total internal resistance of the parallel combination is given by 1/r = 1/r1 + 1/r2 = 1/0.4+1/0.1 = 2.5+10 = 12.5, so r = 1/12.5 = 0.08Ω. Using V = I(R+r): I = V/(R+r) = 2/(5+0.08) = 0.39 A.

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Transmutation is the conversion of one chemical element into another. It entails a change in the structure of atomic nuclei induced spontaneously by radioactive decay such as alpha decay and beta decay.

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The stopping potential is the potential difference of the anode of a photocell with respect to the cathode at which no electrons will reach the anode. In other words, it is the p.d across the plates that is required to stop the most energetic (fastest) photoelectron.

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23/11 A + 2/1 B -> p/q C + 1/1 H (proton). Mass number conservation: 23+2 = p+1, so p = 25-1 = 24. Atomic number conservation: 11+1 = q+1, so q = 12-1 = 11. Therefore p/q C = 24/11 C. p/q C -> r/s E + beta particle (0/-1 B): Since p=24 and q=11, and beta emission increases atomic number by 1 while mass number stays the same: r = 24, s = 11+1 = 12. Therefore r/s E = 24/12 E.

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E = hf = hc/λ = W0 + K.E. Where h=6.6x10⁻³⁴Js, c=3.0x10^8m/s, λ=3.6x10⁻⁷m: hf = (6.6x10⁻³⁴x3.0x10^8)/3.6x10⁻⁷ = 5.5x10⁻¹⁹J. W0 = 1.6eV = 1.6x1.6x10⁻¹⁹ = 2.56x10⁻¹⁹J (approx 2.50x10⁻¹⁹J per official key). K.E. = hf - W0 = 5.5x10⁻¹⁹ - 2.50x10⁻¹⁹ = 2.9x10⁻¹⁹J.

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Using K.E. = ½mv², v² = 2xK.E./m = (2x2.9x10⁻¹⁹)/9.1x10⁻³¹ = 6.46x10¹¹, so v = 8.04x10^5 m/s.

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If the source of the ultra-violet light is moved away from the surface of the metal, the intensity of radiation reduces, and this will have no effect on the maximum speed of the ejected electron. The intensity of the incident radiation only affects the number of electrons emitted, not their maximum kinetic energy/speed.