All 50 questions from the West African Examinations Council (WAEC) Physics 2013 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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The rising of a liquid in an open ended glass tube of narrow bore is due to
Capillarity is the tendency of a liquid to rise or fall in a narrow tube (capillary). A capillary is an open-ended glass tube.
Which of the following units is equivalent to the Watt?
Watt is the SI unit of power. Power = force × velocity = mass × acceleration × velocity. Therefore Watt = kg × ms⁻² × ms⁻¹ = kgm²s⁻³.
Which of the following statements about pressure in a liquid is correct?
Pressure in a liquid increases in magnitude with depth. Pressure at any point acts in all directions, and depends on depth, density and gravity.
A block of wood of mass 5kg is pulled on a platform by a force 40N as illustrated in the diagram above. If the frictional force, F experienced by the block is 12N, calculate the magnitude of the acceleration of the block.
Net force = P − F = 40 − 12 = 28N. Acceleration a = F(net)/m = 28/5 = 5.6ms⁻².
Solid friction, like viscosity, is
Both solid friction and viscosity oppose relative motion between surfaces/layers.
The slope of a linear distance-time graph represents
The slope of a distance-time graph gives speed (the slope of a displacement-time graph gives velocity).
A body of mass 2kg is released from rest on a smooth plane inclined at an angle of 60° to the horizontal. Calculate the acceleration of the body down the plane. [g = 10ms⁻²]
On a smooth inclined plane, the only force acting down the plane is the component of gravity parallel to the plane: a = g sinθ = 10 × sin60° = 8.7ms⁻².
The total area under a force-velocity graph represents
Power = force × velocity, so the area under a force-velocity graph (force on one axis, velocity on the other) represents power.
Use the following information to answer questions 9 and 10. A body of mass 20g projected vertically upwards in vacuum returns to the point of projection after 1.2s. [g=10ms⁻²] Calculate the speed of projection.
Time of flight T = 1.2s, so time to reach maximum height t = T/2 = 0.6s. Using v = u − gt with v=0 at max height: 0 = u − (10)(0.6), so u = 6.0ms⁻¹.
(Using the same information as Q9) Determine the potential energy of the body at the maximum height of its motion.
P.E at maximum height = K.E at projection = ½mu² = ½ × 0.02 × 6² = 0.36J.
Four co-planar forces of magnitudes 10N, 17N, 6N and 20N act at point O as shown in the diagram above. Determine the magnitude of the resultant force.
Vertical component = (10−6)N = 4N. Horizontal component = (20−17)N = 3N. Resultant R = √(4²+3²) = √25 = 5N.
The maximum displacement on either side of the equilibrium position of an object in simple harmonic motion represents
The amplitude is the maximum displacement on either side of the equilibrium position.
From Newton's first law of motion,
Newton's first law implies that a body at constant velocity (including at rest) has zero net force acting on it. The addition of all forces on it sums to zero — that does not mean no forces act on it.
A body of mass 11kg is suspended from a ceiling by an aluminium wire of length 2m and diameter 2mm. Calculate the elastic energy stored in the wire [Young's modulus of aluminium = 7.0×10¹⁰Nm⁻²; g=10ms⁻², π=3.14]
Force on wire = weight = mg = 110N. Cross-sectional area = πd²/4 = 3.14×(2×10⁻³)²/4 = 3.14×10⁻⁶m². Extension e = Force×length/(Area×Y) = (110×2)/(3.14×10⁻⁶×7.0×10¹⁰) = 1×10⁻³m. Elastic energy E = ½Fe = ½×110×1×10⁻³ = 5.5×10⁻²J.
The velocity ratio of an inclined plane
V.R = 1/sinθ. As θ decreases (first quadrant, θ≤90°), sinθ decreases, so V.R increases. Thus V.R increases with a decrease in the angle of inclination.
Which of the following types of thermometers is used for the calibration of other thermometers?
Constant volume gas thermometers are very sensitive, consistent and have a wide range. They are also accurate, and due to this, they are used for calibrating other thermometers.
The magnitude of the expansion or contraction of a substance depends on the I. temperature change. II. nature of the substance. III. size of the substance. Which of the statements above are correct?
The magnitude of thermal expansion/contraction of a substance depends on the temperature change, the nature (material) of the substance, and its size.
Highly polished silvery surfaces are
Highly polished silvery surfaces are poor absorbers and poor emitters of radiation; dull, black surfaces are better absorbers and emitters of radiation.
The volume of a given mass of gas at 27°C and 800 mmHg is 76 cm³. Calculate its volume at s.t.p.
Using the general gas law: P1V1/T1 = P2V2/T2, with T1=300K, P1=800mmHg, V1=76cm³, T2=273K, P2=760mmHg: V2 = (800×76×273)/(300×760) = 72.8 cm³.
The outlet of a bicycle pump is used to inflate a football as illustrated in the diagram above. Why does the pressure of the air inside the pump increase as the pump handle is slowly pushed downward at constant temperature?
When the pump handle is pushed down, the volume of the air in the pump decreases, causing more collisions between the air molecules and the pump's interior walls, increasing pressure. (The collisions responsible are between the air molecules and the walls, not between the air molecules themselves.)
Ice of mass 10g at −5°C was completely converted to water at 0°C. Calculate the quantity of heat used. [Specific heat capacity of ice = 2.1Jg⁻¹K⁻¹, specific latent heat of fusion of ice = 336Jg⁻¹]
Heat needed = heat to warm ice from −5°C to 0°C + heat to melt ice at 0°C = mcΔT + mLf = (10×2.1×5) + (10×336) = 105 + 3360 = 3465J.
An electric heater has a resistance of 50Ω. When it is immersed in water and connected to mains source, it draws a current of 4.0A. Calculate the heat gained by the water if the heater is switched on for 2 minutes, assuming no heat losses to the surroundings.
Power = I²R = 4²×50 = 800W. Time = 2×60 = 120s. Heat gained = Power×time = 800×120 = 96000J.
When salt is dissolved in water, the freezing point of the water
Dissolving salt in water lowers (decreases) its freezing point — this is freezing-point depression.
The diagram above illustrates a waveform. Which of the points on the waveform are in phase?
Points that are the same vertical distance from the main line and moving in the same direction are in phase. P and T both lie on the main line moving in the same direction, so they are in phase.
The equation of a certain progressive transverse wave is y = 2sin2π(t/0.01 − x/30), where x and y are in cm and t in seconds. Calculate the period of the wave.
Comparing with the standard form y = Asin2π(t/T − x/λ), the period T = 0.01s.
At which position should an object be placed in front of a concave mirror in order to obtain an image which is of the same size as the object?
When an object is placed at the centre of curvature of a concave mirror, the image formed is also at the centre of curvature, real, inverted, and the same size as the object.
Images formed by a convex mirror are always
A convex mirror always forms a virtual, erect and diminished image located behind the mirror, regardless of the object's position.
The refractive index of a material is 1.5. Calculate the critical angle at the glass-air interface.
sinC = 1/n = 1/1.5 = 0.67. C = sin⁻¹0.67 = 42°.
A diverging lens of focal length 30cm produces an image 20cm from the lens. Determine the object distance.
For a diverging lens, f=−30cm, v=−20cm (virtual image). Using 1/f = 1/u + 1/v: −1/30 = 1/u − 1/20; 1/u = 1/30+1/20 = 0.0167; u = 60cm.
Which of the following statements about the Galilean telescope is not correct?
In a Galilean telescope, the final image is erect and virtual, not inverted — so statement A is the incorrect one.
Which of the following radiations has its frequency lower than that of infra-red radiation?
In the electromagnetic spectrum, radio waves have the lowest frequency, lower than infra-red.
A string under tension produces a note of frequency 14 Hz. Determine the frequency when the tension is quadrupled.
Frequency f ∝ √Tension. If tension is quadrupled (4T), new frequency = √4 × original = 2×14 = 28Hz.
Which of the following statements about waves in pipes is correct?
Closed pipes (closed at one end) only support odd harmonics (f, 3f, 5f...); open pipes produce all harmonics.
When a person holds a negatively charged metal rod and stands bare-footed on the ground, how will the charges leak?
The excess negative charges on the rod/person will flow through the body to the ground, where they can disperse.
A charge of 2.0×10⁻⁵C experiences a force of 80N in a uniform electric field. Calculate the magnitude of the electric field intensity.
E = F/q = 80/(2.0×10⁻⁵) = 4×10⁶ N/C.
An electric circuit is connected as illustrated above (three 2V cells in parallel, connected to a 2Ω resistor). Determine the equivalent Emf and current flowing through the circuit respectively, neglecting the internal resistance of the cells.
Since the three cells are connected in parallel, the equivalent emf equals that of one cell: E = 2V (the potential difference/emf across any number of cells connected in parallel is the same as that across each of them). Current I = V/R = 2/2 = 1.0A.
A potential difference of 12V is applied across the ends of a 6Ω resistor for 10 minutes. Determine the quantity of heat generated.
Time = 10 minutes = 600s. Quantity of heat generated = (V²/R)×time = (12²/6)×600 = 24×600 = 14,400 J.
A galvanometer of internal resistance 10Ω has a full scale deflection with a current of 10 mA. Calculate the magnitude of the resistance required to convert it to a voltmeter capable of measuring up to 3V.
Using V = I(Rg+R): 3 = 10×10⁻³×(10+R); 300 = 10+R; R = 290Ω.
Which of the following instruments is used to determine the accurate value of the electromotive force of a cell?
A potentiometer is used to determine the accurate (true) emf of a cell, since at balance it draws no current from the cell.
The direction of motion of a current-carrying conductor placed within the opposite poles of a magnet is determined using
Fleming's left-hand rule: if the thumb, forefinger and middle finger of the left hand are held mutually at right angles, with the forefinger pointing in the direction of the magnetic field and the middle finger in the direction of current, the thumb points in the direction of motion (force).
Two straight current-carrying conductors are placed near each other. Which of the following diagrams correctly illustrates the magnetic field pattern formed by the conductors?
Diagram D correctly shows the magnetic field pattern of two parallel current-carrying conductors, with the fields merging/interacting between the conductors as expected.
The capacitance of parallel plates capacitors varies
Capacitance C = εA/d. As the separation distance d between the plates increases, capacitance decreases — C is inversely proportional to d.
Which of the following devices works on the principle of electromagnetic induction?
Electromagnetic devices working on the principle of electromagnetic induction include the electric bell, telephone earpiece, magnetic relay, circuit breaker, and carbon microphone.
Which of the following devices does not make use of eddy current for its action?
Applications of eddy current include the induction furnace, the speedometer, the moving-coil galvanometer (damping), the sensitive mass balance, the breaker in large electric motors, and crack detection in railway tracks. (Per the printed answer key, the option identified as not using eddy current is D.)
A coil of inductance 0.12H and resistance 4Ω, is connected across a 240V, 50Hz supply. Calculate the current through it. [π=3.14]
XL = 2πfL = 2×3.14×50×0.12 = 37.68Ω. Impedance Z = √(R²+XL²) = √(4²+37.68²) ≈ 37.9Ω. Current I = V/Z = 240/37.9 = 6.33A ≈ 6.3A.
The work function of a metal is 2.56×10⁻¹⁹ J. Calculate the frequency of a photon whose energy is required to eject from the metal an electron with kinetic energy of 3.0 eV. [1eV=1.6×10⁻¹⁹ J; h=6.6×10⁻³⁴Js]
Energy of photon = work function + K.E of electron = 2.56×10⁻¹⁹ + (3.0×1.6×10⁻¹⁹) = 7.36×10⁻¹⁹J. Frequency f = E/h = 7.36×10⁻¹⁹/6.6×10⁻³⁴ = 1.12×10¹⁵Hz.
The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with electromagnetic radiation of suitable frequency is called
The minimum energy needed to liberate/eject an electron from a metal surface is called the work function (distinct from ionization energy, which removes the most loosely bound electron from a gaseous atom).
Which of the following particles are termed nucleons in a neutral atom?
Nucleons are the particles found in the nucleus of an atom — protons and neutrons.
Which of the following statements about the use of radioisotopes is not correct? They are used to
The uses of radioisotopes include: radiotherapy; as tracers to check blood circulation, detect leaks in underground pipes, and trace metabolic processes in plants/animals; quality control (measuring paper thickness); tracing cracks in metals or bones; food preservation; and radioactive dating/age estimation. Per the printed answer key, the statement identified as incorrect is option A.
Which of the following phenomena supports the theory that waves have a particle nature?
The photoelectric effect supports the particle (photon) nature of light/waves.
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