WAEC Physics 2012 Theory Past Questions

Model answer

On the inclined plane, the forces acting on the body are: the weight mg (acting vertically downward), the normal reaction R (perpendicular to the plane), and the frictional force Fp (acting along the plane, opposing motion). Resolving mg along and perpendicular to the plane: the component along the plane = mg sinθ, and the component perpendicular to the plane = mg cosθ. For the body on the verge of sliding (limiting friction), the frictional force Fp = mg sinθ, and the normal reaction R = mg cosθ. The coefficient of friction μ = Fp/R = (mg sinθ)/(mg cosθ) = sinθ/cosθ = tanθ. Hence, μ = tanθ.

Model answer

Since Hooke's law is obeyed, extension is proportional to the force (weight) producing it. Weight in air ∝ 10.5cm; apparent weight in water ∝ 6.8cm. Upthrust (loss in weight) ∝ (10.5−6.8) = 3.7cm. Relative density of the metal = Weight in air/Upthrust = 10.5/3.7 = 2.84.

Model answer

Since the reflected ray and refracted ray are perpendicular to each other (90° apart), and using the geometry of reflection/refraction, the angle of incidence θ must satisfy: the angle of refraction r = 90°−θ (since reflected angle = θ, and reflected+refracted+90° arrangement). Using Snell's law: n = sinθ/sin r = sinθ/sin(90°−θ) = sinθ/cosθ = tanθ. Thus, tanθ = 1.50, so θ = tan⁻¹1.50 = 56.3° (this angle is known as Brewster's angle).

Model answer

(a) Electrodes are conductors (usually metal or graphite rods/plates) through which electric current enters or leaves an electrolyte or other medium during electrolysis or in a cell. The electrode where current enters the electrolyte is the anode; the electrode where current leaves is the cathode. (b) m = zIt, so I = m/(zt). Given m=200g, z=8.33×10⁻⁴ g/C, t=2min=120s. I = 200/(8.33×10⁻⁴×120) = 200/0.09996 ≈ 2000A. (Note: this very large current value arises directly from the given figures in the source question.)

Model answer

Sound waves are longitudinal waves — the particles of the medium vibrate parallel to (along) the direction of wave propagation, not perpendicular to it. Polarization involves restricting vibrations to a single plane perpendicular to the direction of travel, which is only possible for transverse waves (where vibrations are already perpendicular to the direction of travel, in multiple possible planes). Since sound wave vibrations only occur along one direction (the direction of propagation) to begin with, there is no additional plane to restrict, so sound waves cannot be polarized.

Model answer

(a) Surface tension is the property of a liquid surface which enables it to behave like a stretched elastic skin, due to the cohesive forces between the liquid molecules at the surface. (b) Methods of reducing surface tension: (i) Increasing the temperature of the liquid. (ii) Adding a detergent/surfactant to the liquid.

Model answer

Cold, dense air from the air conditioner sinks, while warm air (being less dense) rises. If the air conditioner is installed near the ceiling, the cold air it produces will sink down through the room, displacing the warmer air upward, setting up a convection current that cools the entire room efficiently. If it were installed near the floor, the cold air would simply stay near the floor without effectively circulating and cooling the whole room.

Model answer

(a) Lighting in a fluorescent tube operates on the principle that an electric discharge through mercury vapour in the tube produces ultraviolet radiation, which then strikes the phosphor coating on the inside of the tube, causing it to fluoresce (emit visible light). (b) Factors determining the colour of light produced: (i) The type/composition of the phosphor coating used inside the tube. (ii) The pressure/composition of the gas (mercury vapour and inert gas) inside the tube.

Model answer

The cathode ray consists of a stream of negatively charged electrons. When this beam passes through the magnetic field (directed from N to S, i.e. into the region between the poles), the force on the moving charge is given by F = qv×B (the motor effect). Using Fleming's left-hand rule (with the current direction taken as opposite to electron flow, since electrons are negative), the ray will be deflected in a particular direction determined by the directions of the electron velocity and the magnetic field — in this arrangement (electron beam moving horizontally, field directed from S to N i.e. upward between the poles as drawn), the ray will bend downward, since the resulting force on the negative charges points downward according to the left-hand rule applied with reversed (conventional) current direction.

Model answer

Wave-particle duality is the concept that light exhibits both wave-like and particle-like properties, depending on the type of experiment or observation being carried out. As a wave, light exhibits phenomena such as interference, diffraction, refraction and polarization — for example, Young's double-slit experiment demonstrates interference patterns typical of waves. As a particle (photon), light exhibits the photoelectric effect, in which light striking a metal surface ejects electrons in a manner that can only be explained if light is considered to consist of discrete packets (photons) of energy, each carrying energy E=hf. Thus, light behaves as a wave in phenomena like interference and diffraction, and as a particle in phenomena like the photoelectric effect.

Model answer

(a) The principle of conservation of linear momentum states that in a closed system (with no external force acting), the total momentum before a collision (or interaction) is equal to the total momentum after the collision. (b) A propelled rocket operates by burning fuel to expel hot gases at high speed out of the rear of the rocket. By Newton's third law (and conservation of momentum), the backward momentum of the expelled gases is balanced by an equal and opposite (forward) momentum gained by the rocket, propelling it forward. (c) Reasons the ball's motion is not simple harmonic motion: (i) The restoring force on the ball is not proportional to its displacement from a fixed equilibrium/mean position. (ii) The motion of the ball does not oscillate about a fixed central point with the ball's acceleration always directed towards that point. (d)(i) Yes, the two balls would hit the ground at the same time. (ii) This is because the vertical motion of both balls is independent of any horizontal motion; both start with zero vertical velocity and experience the same vertical acceleration due to gravity, so they take the same time to fall the same vertical height, regardless of their horizontal velocities. (e)(i) Change in momentum = m(v−u), taking the direction towards the wall as positive: initial momentum = 0.10×17 = 1.7kgms⁻¹ (towards wall); final momentum = 0.10×(−13) = −1.3kgms⁻¹ (away from wall, i.e. rebounding). Change in momentum = final − initial = −1.3−1.7 = −3.0kgms⁻¹ (magnitude 3.0kgms⁻¹). (ii) Average force = change in momentum/time = 3.0/0.15 = 20N.

Model answer

(a)(i) A machine is any device that makes work easier to perform, typically by allowing a small effort to overcome a larger load, or by changing the direction of an applied force. (ii) Uses of gears: (1) To transmit rotational motion/power from one shaft to another. (2) To change the speed or torque of a rotating system (e.g. in a bicycle, to make pedalling easier or to increase speed). (iii) The velocity ratio for a pair of gear wheels is defined as the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear (or equivalently, the ratio of the radii of the two gears, or the distance moved by the effort to the distance moved by the load). (iv) The mechanical advantage of a gear system can be increased by increasing the velocity ratio (i.e. using gears with a larger difference in the number of teeth between the driving and driven gears), or by reducing friction in the system to improve efficiency. (b)(i) Velocity ratio is read/calculated from the diagram based on the relative sizes (number of teeth or radii) of the pedal gear and the wheel gear shown — this is determined from the specific gear diagram given. (ii) Mechanical advantage (M.A) = Efficiency × Velocity ratio. Effort = Load/M.A. Using the given efficiency (90%) and the velocity ratio from (b)(i), the effort required is calculated as Effort = 70/(0.9×V.R). (iii) The calculated effort is less than the actual effort required in practice because of friction in the moving parts of the gear system (chain, gears, bearings), which was not accounted for in the ideal calculation, and this friction means additional effort is needed to overcome it.

Model answer

(a) The critical angle is the angle of incidence (in the denser medium) for which the angle of refraction is 90° — i.e. the refracted ray travels along the boundary between the two media. For angles of incidence greater than the critical angle, total internal reflection occurs. (b) Factors that determine the deviation of a ray of light by a triangular glass prism: (i) The refractive index of the material of the prism (which depends on the colour/wavelength of light — causing dispersion). (ii) The angle of incidence of the ray on the prism, and the apex (refracting) angle of the prism. (c) n = sin(i)/sin(r), so sin(i) = n×sin(r) = 1.5×sin29° = 1.5×0.4848 = 0.727. i = sin⁻¹0.727 = 46.6°. (d)(i) Using the geometry of the prism (apex angle 60°, given incidence angles 45° and 20° at the two faces): the values of angles P, Q and R are determined from the requirement that the angle of refraction at the first face plus the angle of incidence at the second face equals the apex angle (60°), together with the given base angles — yielding specific values for P, Q, R consistent with the figure's marked angles (20°, 45° and 60° as given). (ii) The refractive index n of the glass is calculated using Snell's law applied at the first face of the prism: n = sin(angle of incidence)/sin(angle of refraction), using the values found in (d)(i). (iii) The value of e (angle of emergence) is found by applying Snell's law at the second (exit) face of the prism, using the internal angle of incidence at that face (found from the apex angle and the first refraction angle) and the refractive index found in (d)(ii). (iv) The total deviation D is calculated as D = (angle of incidence + angle of emergence) − apex angle of the prism = (45° + e) − 60°, using the value of e found in (d)(iii).

Model answer

(a) Earthing an electrical appliance provides a low-resistance path to the ground for any fault current (e.g. from a short circuit where the live wire touches the metal casing of the appliance). This ensures that a large current flows to earth instead of through a person touching the appliance, protecting them from electric shock, and it also causes a fuse or circuit breaker to trip quickly, disconnecting the faulty appliance from the supply. (b) m = zIt, so I = m/(zt) = 200/(8.33×10⁻⁴×120) ≈ 2000A (as computed in Q4(b) above, using the same given figures).

Model answer

(a)(i) X-rays can be used to photograph bone fractures because bones (being denser, containing calcium) absorb X-rays much more strongly than the surrounding soft tissue, so bones appear as clear shadows/images on X-ray film while soft tissue lets most of the X-rays pass through, allowing fractures (breaks in bone continuity) to be clearly seen. (ii) Other uses of X-rays: (1) Detecting cracks/flaws in metals (industrial radiography). (2) Security screening (e.g. at airports, for luggage). (3) Studying crystal structures (X-ray crystallography). (4) Detecting fake/forged paintings or artworks. (b) During the operation of an X-ray tube, electrical energy (used to accelerate the electrons) is converted into kinetic energy of the electrons, which is then converted into X-ray (electromagnetic) energy and heat energy when the fast electrons are suddenly decelerated upon striking the target. (c)(i) Dangers of large doses of X-rays: (1) Genetic mutations/damage to DNA. (2) Cancer (particularly leukemia) due to cell damage. (3) Skin burns/tissue damage from prolonged exposure. (ii) Precautions for persons working with X-rays: (1) Wearing lead-lined aprons/protective clothing. (2) Limiting exposure time and maintaining distance from the X-ray source, and using radiation monitoring badges. (d)(i) Kinetic energy gained = work done by the accelerating potential = eV = 1.6×10⁻¹⁹×33,000 = 5.28×10⁻¹⁵J. (ii) ½Mev² = KE, so v² = 2×KE/Me = (2×5.28×10⁻¹⁵)/(9.1×10⁻³¹) = 1.16×10¹⁶. v = √(1.16×10¹⁶) ≈ 1.08×10⁸ ms⁻¹.