WAEC SSCE - Physics - 2011

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The emf induced in a wire moving at right angles to a magnetic field is given by the equation: emf = B × l × v where B is the magnetic flux density, l is the length of the wire, and v is the velocity of the wire. Plugging in the given values, we have: emf = 0.4T × 0.3m × 2ms^-1 = 0.24V Therefore, the emf induced in the wire is 0.24V. The correct option is: 0.24V

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Power, P = work done (W) / time interval (t) We know that, work done (W) = force (F) x distance (d) Therefore, power (P) = (F x d) / t Rearranging this equation, we get: t = (F x d) / P Substituting the given values, we get: t = (20 N x 500 m) / 0.4 kW t = 25,000 s Therefore, the time interval during which the force is applied is 25,000 seconds. Answer: 25.0s

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X-rays are electromagnetic waves that are produced when high-speed electrons are stopped by a metal target. They have many useful properties such as traveling in straight lines, traveling at the speed of light, and affecting photographic films. X-rays, however, are not affected by magnetic fields, meaning they cannot be deflected by a magnetic field. Therefore, the property that is not applicable to X-rays is that they are deflected by magnetic fields.

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Total internal reflection occurs in an optical prism when light rays are incident in the prism at an angle greater than the critical angle. When a light ray travels from an optically denser medium (like a glass prism) to a less dense medium (like air), it bends away from the normal line. As the angle of incidence increases, the angle of refraction also increases until it reaches a certain angle called the critical angle. If the angle of incidence is greater than the critical angle, the light ray is totally reflected back into the denser medium, which is known as total internal reflection. This phenomenon is used in various optical devices such as prisms, optical fibers, and reflecting telescopes.

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The area under a velocity-time graph represents the distance covered by an object. Velocity is the rate of change of displacement with time. Therefore, the area under the velocity-time graph is equal to the displacement covered by the object during the given time interval. This is because the area under the graph is the product of the time interval and the average velocity during that time interval, which is equal to the distance traveled. So, the correct option is "distance covered".

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The formula to calculate the image distance for a converging lens is: 1/f = 1/do + 1/di where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. Substituting the given values: 1/15 = 1/20 + 1/di Simplifying and solving for di: di = 60 cm Therefore, the image distance is 60.0cm. Answer: Option D.

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The threshold frequency in photoelectric emission is the minimum frequency of incident radiation required to eject electrons. This means that if the frequency of the incident radiation is below the threshold frequency, no electrons will be emitted, regardless of the intensity or duration of the radiation. However, if the frequency of the incident radiation is equal to or greater than the threshold frequency, electrons will be emitted, and their kinetic energy will increase with increasing frequency. Therefore, the correct option is "minimum frequency of incident radiation required to eject electrons."

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The absolute refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. Therefore, the formula for the absolute refractive index of the medium is: \[\text{Absolute refractive index} = \frac{\text{Speed of light in vacuum}}{\text{Speed of light in the medium}} = \frac{C}{V}\] Therefore, the answer is \(\frac{C}{V}\).

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We can solve this problem using kinematic equations of motion. Since the motion is projectile motion, we can break it into two components, horizontal and vertical. In the horizontal direction, there is no acceleration, so the velocity remains constant throughout the motion. In the vertical direction, the coin is moving upward against the force of gravity, which causes it to slow down, then come to rest at the highest point before falling downward. The time taken to reach the highest point can be calculated using the vertical component of the initial velocity and acceleration due to gravity. Using the equation: v = u + at where: v = final velocity = 0 (at the highest point) u = initial velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point Solving for t, we get: t = u/a = 15.0/10 = 1.5s The maximum height reached by the coin can be calculated using the equation: s = ut + 0.5at^2 where: s = maximum height reached u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point = 1.5s Solving for s, we get: s = 0 + 0.5 x 10 x (1.5)^2 = 11.25m Now, the coin falls from the maximum height and hits the floor. The time taken to fall from the maximum height can be calculated using the equation: s = ut + 0.5at^2 where: s = height of the bench = 1.5m u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to fall from maximum height Solving for t, we get: 1.5 = 0 + 0.5 x 10 x t^2 t^2 = 0.3 t = sqrt(0.3) = 0.55s (ignoring the negative root) Now, we can calculate the horizontal distance traveled by the coin during the time it was in the air using the equation: s = ut + 0.5at^2 where: s = horizontal distance traveled u = initial horizontal velocity = 15.0ms^-1 a = acceleration in horizontal direction = 0 (no acceleration) t = time taken to fall from maximum height = 0.55s Solving for s, we get: s = 15.0 x 0.55 = 8.25m Therefore, the distance from the foot of the bench to the point of impact with the floor is approximately 8.25m. Answer: 8.22m (rounding off to two decimal places)

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The image formed by a convex mirror is always virtual, erect and diminished. A convex mirror is a diverging mirror, meaning that it spreads out the light rays that enter it. The image formed by a convex mirror is virtual, which means that it cannot be projected onto a screen. It is always upright or erect, which means that it is not inverted like the image formed by a concave mirror. The image formed by a convex mirror is always smaller than the object, hence diminished.

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Ether produces a cooling effect when it is poured on the hand because it has a high latent heat of vaporization. Latent heat is the energy absorbed or released during a phase change. When ether is poured on the hand, it quickly evaporates due to its low boiling point. As it evaporates, it absorbs heat energy from the hand to overcome the intermolecular forces holding the liquid together, causing a cooling effect on the skin. The higher the latent heat of vaporization, the greater the cooling effect. Therefore, "high latent heat of vaporization" is the correct answer.

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The correct option is: "it is formed by actual intersection of rays." Explanation: When an object is placed in front of a plane mirror, its image is formed behind the mirror. The image formed is virtual, which means that it cannot be projected onto a screen. It is laterally inverted, which means that left appears as right and right appears as left. The size of the image is the same as that of the object, and therefore, it has unit magnification. The distance of the image from the mirror is the same as the distance of the object from the mirror, and therefore, the last statement is also true. However, the image is not formed by actual intersection of rays as the rays of light do not actually converge at the position of the image. The image is formed due to the reflection of light from the mirror's surface.

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This is a problem involving the mechanical advantage of a simple machine. The machine in question is a wheel and axle. The effort required to lift a load is dependent on the mechanical advantage of the machine. The mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle. In this case, the mechanical advantage is: MA = radius of wheel / radius of axle = 30 cm / 6 cm = 5 This means that for every unit of effort applied to the machine, it can lift 5 units of load. Using this information, we can determine the effort required to lift a load of 120.0 N by setting up the equation: MA = load / effort Solving for effort, we get: effort = load / MA = 120.0 N / 5 = 24.0 N Therefore, the effort required to lift a load of 120.0 N using this machine with 100% efficiency is 24.0 N. The correct answer is (c) 24.0N.

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The unit of capacitance is farad, which is represented by the symbol F. Capacitance is the ability of a capacitor to store electric charge per unit voltage applied. One farad of capacitance is defined as the capacitance of a capacitor that stores one coulomb of charge when a potential difference of one volt is applied across it. In simpler terms, it is a measure of the amount of electrical charge that can be stored in a capacitor for a given voltage.

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The correct relationship between "G" and "g" in a gravitational field is given by the equation g = \(\frac{GM}{R^2}\), where g represents the acceleration due to gravity, G is the gravitational constant, M is the mass of the attracting body, and R is the distance between the centers of mass of the two objects. This equation is known as Newton's law of gravitation and states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The acceleration due to gravity at any point is the gravitational force experienced by a unit mass at that point. The gravitational constant G is a fundamental constant of nature and is considered to be one of the most accurately measured physical constants.

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The statement that is not correct is: "molecules of ice, water and water vapour have equal intermolecular distances." Explanation: - Ice, water, and water vapour are different states of water. They have different intermolecular distances because the intermolecular forces between their molecules are different. - In ice, the intermolecular forces are the strongest due to hydrogen bonding, which results in a rigid and orderly arrangement of water molecules with a fixed intermolecular distance. - In liquid water, the intermolecular forces are weaker than in ice, and the intermolecular distance is more variable. - In water vapour, the intermolecular forces are weakest among the three, and the intermolecular distance is the largest. Therefore, the statement that molecules of ice, water and water vapour have equal intermolecular distances is not correct.

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The equation that relates mass and energy is E=mc². Here, the change in mass is given as 2.0 x 10^-27 kg. The speed of light is given as 2.0 x 10⁸ ms^-1. Substituting these values in the equation, we get: E = (2.0 x 10^-27 kg) x (2.0 x 10⁸ ms^-1)² E = 1.8 x 10^-10 J Therefore, the amount of energy released is 1.8 x 10^-10 J.

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The resistivity, \(\mathit{P}\), of a material is a measure of its ability to resist the flow of electric current. The resistance, R, of a material is directly proportional to its length, l, and inversely proportional to its cross-sectional area, A. Therefore, we can say that \(\mathit{P} = \frac{RA}{l}\), as this equation combines the resistance, length, and cross-sectional area to give the resistivity of the material.

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The property of a fluid that is used to determine its suitability as a lubricant is its viscosity. Viscosity is a measure of a fluid's resistance to flow or deformation, and it is directly related to its thickness or consistency. The thicker the fluid, the higher its viscosity, and the more effective it is at providing lubrication and reducing friction between two surfaces. Therefore, high viscosity fluids are preferred as lubricants since they provide better lubrication, while low viscosity fluids are preferred as coolants.

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The correct statement that defines a simple machine is: "a device with which work can be done easily". A simple machine is any mechanical device that can change the magnitude or direction of an applied force, making it easier to move or lift an object. Examples of simple machines include levers, pulleys, inclined planes, screws, and wheel and axle systems. These machines work by reducing the amount of force required to do a certain amount of work, allowing humans to accomplish tasks that would otherwise be difficult or impossible to perform. Therefore, option C is the correct answer.

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In the absence of gravitational force, the weight of the body is zero. This is because weight is the force with which a body is attracted towards the center of the Earth or any other massive body. In the absence of such a force, the body will not experience any weight. However, the mass of the body remains the same, as it is a measure of the amount of matter contained in the body. Therefore, - zero - is the correct answer.

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The capacitance of a parallel-plate capacitor is the ratio of the magnitude of the charge on either plate to the potential difference between them. The capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them. Thus, as the separation between the plates decreases, the capacitance increases. The capacitance is also directly proportional to the permittivity of the dielectric material between the plates. A dielectric is an insulating material that can be placed between the plates of a capacitor to increase its capacitance. The permittivity of the dielectric material is a measure of its ability to store electrical energy in an electric field. Thus, adding a dielectric between the plates of a parallel-plate capacitor increases the capacitance. Therefore, the correct answer is: the capacitance of a parallel-plate capacitor is greater with a dielectric material between the plates than without a dielectric.

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Uranium-234 and Thorium-230 are both radioactive isotopes, meaning they undergo spontaneous nuclear decay. In this case, Uranium-234 disintegrates to form Thorium-230 by emitting an alpha particle. An alpha particle is a helium nucleus, consisting of two protons and two neutrons, which is ejected from the nucleus during alpha decay. This results in the atomic number of the daughter nucleus being reduced by 2 and the mass number being reduced by 4. So, is correct.

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The momentum of an object is defined as the product of its mass and velocity. Mathematically, this can be expressed as p = mv, where p is momentum, m is mass and v is velocity. Using the given values, we can calculate the momentum of the object as follows: p = mv = 5.0 kg x 10ms^-1 = 50.0 kgms^-1 Therefore, the momentum of the object is 50.0 kgms^-1. Answer: 50.0 kgms^-1

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The assumption that is not valid for an ideal gas is that the "force of attraction between molecules is negligible." This assumption is not valid for real gases since molecules have intermolecular forces of attraction. In an ideal gas, it is assumed that the gas particles have no intermolecular forces of attraction, meaning that they do not attract or repel each other, and they move independently. However, in reality, all gases have some degree of intermolecular forces of attraction.

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When two sound waves of different frequencies overlap, they interfere with each other to produce a resultant wave. If the frequencies of the two waves are close, a phenomenon called beats occurs, where the amplitude of the resultant wave varies periodically. The period of beats is given by T = 1/(f1 - f2), where f1 and f2 are the frequencies of the two waves. Using the formula, we can calculate the beats period for the given frequencies: T = 1/(12 Hz - 10 Hz) = 1/2 Hz = 0.5 s Therefore, the answer is 0.5s.

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(a) The force causing the spring to shrink in fig.(b)

When the load is lowered into the water it experiences an upthrust (buoyant force) from the water, acting vertically upwards. This upthrust partly supports the weight of the load, so the tension pulling on the spring is reduced and the spring contracts (shrinks). The force responsible for the shrink is therefore the upthrust of the water on the load.

(b) Work done by the force in causing the shrink

Reading the contraction from the metre rule. The pointer attached to the load marks the position of the lower end of the spring against the fixed rule:

• In air (fig. a) the pointer reads \(20\ \text{cm}\) (the spring is fully stretched by the whole weight \(W_a\)).
• In water (fig. b) the upthrust lifts the load, so the pointer rises to \(18\ \text{cm}\).

The contraction (shrink) of the spring is the difference of the two readings:

\[x = 20\ \text{cm}-18\ \text{cm}=2\ \text{cm}=2\times10^{-2}\ \text{m}.\]

Work done. For a spring obeying Hooke's law, the work done in changing its length by \(x\) against a force constant \(k\) is

\[W=\tfrac{1}{2}kx^{2}.\]

With \(k=2.0\times10^{11}\ \text{N m}^{-1}\) and \(x=2\times10^{-2}\ \text{m}\):

\[W=\tfrac{1}{2}\times(2.0\times10^{11})\times(2\times10^{-2})^{2}\]

\[W=\tfrac{1}{2}\times(2.0\times10^{11})\times(4\times10^{-4})\]

\[W=\mathbf{4.0\times10^{7}\ \text{J}}.\]

The key step is to read \(x\) as the difference of the two rule readings (\(20\ \text{cm}\) in air and \(18\ \text{cm}\) in water), giving \(x = 2\ \text{cm}\), and only then substitute into \(W=\tfrac12 kx^{2}\).

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(a)(i) Transmutation: Transmutation is the change of one element into another as a result of a nuclear reaction, in which the number of protons in the nucleus (the atomic number) changes, for example during radioactive decay or artificial nuclear bombardment.

(a)(ii) Stopping potential: The stopping potential is the minimum negative (retarding) potential that must be applied to the collecting electrode of a photocell to just stop the most energetic photoelectrons from reaching it, so that the photocurrent becomes zero. \(eV_s = KE_{max}\).

(b) Nuclear equations:

\[ {}^{23}_{11}A + {}^{2}_{1}B \rightarrow {}^{p}_{q}C + {}^{1}_{1}\text{(proton)}. \]

Conserving nucleon number: \(23 + 2 = p + 1 \Rightarrow p = 24\). Conserving charge: \(11 + 1 = q + 1 \Rightarrow q = 11\).

\[ {}^{24}_{11}C \rightarrow {}^{r}_{s}E + {}^{0}_{-1}\beta. \]

Conserving nucleon number: \(24 = r + 0 \Rightarrow r = 24\). Conserving charge: \(11 = s + (-1) \Rightarrow s = 12\).

Therefore \(p = 24,\; q = 11,\; r = 24,\; s = 12\).

(c) Energy of the incident photon:

\[ E = \frac{hc}{\lambda} = \frac{(6.6\times10^{-34})(3.0\times10^{8})}{3.6\times10^{-7}} = 5.5\times10^{-19}\,\text{J}. \]

Work function \(W_0 = 1.6\,\text{eV} = 1.6\times(1.6\times10^{-19}) = 2.56\times10^{-19}\,\text{J}\).

(i) Maximum kinetic energy:

\[ KE_{max} = E - W_0 = 5.5\times10^{-19} - 2.56\times10^{-19} = 2.94\times10^{-19}\,\text{J}. \]

(ii) Speed of the emitted electron: from \(KE = \tfrac{1}{2}mv^{2}\),

\[ v = \sqrt{\frac{2\,KE}{m}} = \sqrt{\frac{2\times2.94\times10^{-19}}{9.1\times10^{-31}}} = \sqrt{6.46\times10^{11}} \approx 8.04\times10^{5}\,\text{m s}^{-1}. \]

(d) Moving the source of ultra-violet light farther from the metal only reduces the intensity (number of photons per second arriving), so fewer electrons are emitted per second. It does not change the frequency/energy of each photon, so the maximum kinetic energy and hence the maximum speed of the ejected electron remain unchanged.

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For a projectile launched horizontally, the horizontal and vertical motions are independent.

Step 1 - find the time of flight from the horizontal motion. Horizontally the speed is constant at \(u = 4\,\text{m s}^{-1}\):

\[ R = u\,t \;\Rightarrow\; 25 = 4t \;\Rightarrow\; t = 6.25\,\text{s}. \]

Step 2 - find the height from the vertical motion. The stone starts with zero vertical velocity and falls freely:

\[ h = \tfrac{1}{2} g t^{2} = \tfrac{1}{2}\times10\times(6.25)^{2}. \]

\[ h = 5\times39.06 \approx 195.3\,\text{m}. \]

The height of the tower is approximately 195.3 m.

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(a)(i) Eclipse: An eclipse is the total or partial disappearance of a heavenly body (the sun or the moon) from view, caused when the shadow of one body falls on another as the sun, earth and moon come to lie nearly in a straight line.

(a)(ii) Three types of eclipse:

• Eclipse of the sun (solar eclipse)
• Eclipse of the moon (lunar eclipse)
• Annular eclipse

(b)(i) Eye defect: The student sees distant objects (the board) clearly but cannot focus on near objects (the book), so the defect is long sight (hypermetropia).

(b)(ii) Correcting lens: A convex (converging) lens.

(b)(iii) Power of the lens: \(f = 10\,\text{cm} = 0.10\,\text{m}\).

\[ P = \frac{1}{f} = \frac{1}{0.10} = +10\,\text{D (dioptres)}. \]

(c) Distance between the cars: The ultrasonic beep travels from B to A and is reflected back to B, so it covers a total path of \(2d\) in \(t = 5.6\times10^{-3}\,\text{s}\).

\[ 2d = vt = 340\times5.6\times10^{-3} = 1.904\,\text{m}, \]

\[ d = \frac{1.904}{2} = 0.952\,\text{m}. \]

The two cars are 0.952 m apart at that instant.

(d) Focal length of the convex mirror: The image is virtual, formed \(9\,\text{cm}\) behind the mirror, so \(v = -9\,\text{cm}\). The magnification \(m = \dfrac{-v}{u} = 0.6\) gives \(u = \dfrac{9}{0.6} = 15\,\text{cm}\).

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-9} + \frac{1}{15} = -0.1111 + 0.0667 = -0.0444, \]

\[ f = -22.5\,\text{cm}. \]

The focal length of the convex mirror is 22.5 cm, the negative sign confirming that it is a diverging (convex) mirror.

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Three properties of cathode rays which suggest the particle (corpuscular) nature of matter are:

1. They travel in straight lines and cast sharp shadows of objects placed in their path, as would a stream of moving particles.
2. They are deflected by electric and magnetic fields, showing that they consist of charged particles (electrons carrying negative charge) that possess mass and charge.
3. They possess momentum and kinetic energy - they can exert a mechanical force, for example turning a small paddle wheel placed in their path, which shows the moving stream carries the properties of particles.

(They also produce heat on striking a target and can be deflected/behave as though made of discrete massive particles.)

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The shape of a meniscus depends on the relative strengths of two forces: cohesion (the attraction between molecules of the same liquid) and adhesion (the attraction between the liquid molecules and the molecules of the glass).

Water (concave meniscus): For water in a glass tube, the adhesive force between water and glass is greater than the cohesive force between the water molecules. The water is therefore pulled up the walls of the tube, wetting the glass, and its surface curves upward at the edges to give a concave meniscus.

Mercury (convex meniscus): For mercury, the cohesive force between the mercury molecules is greater than the adhesive force between mercury and glass. The mercury therefore does not wet the glass; it is pulled together and depressed at the walls, so its surface bulges upward in the middle to give a convex meniscus.

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Three methods of polarizing an unpolarized beam of light are:

1. Polarization by reflection - when ordinary light is reflected from a transparent surface (for example water or glass) at the polarizing (Brewster) angle, the reflected light becomes plane polarized.
2. Polarization by selective absorption (using a polaroid/dichroic material) - a polaroid sheet transmits vibrations in only one plane and absorbs those in all other planes, producing plane polarized light.
3. Polarization by double refraction (using a doubly-refracting crystal such as calcite/Nicol prism) - the crystal splits the light into two plane polarized rays vibrating in mutually perpendicular planes.

(Polarization by scattering, as occurs with sunlight in the atmosphere, is also acceptable.)

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(a) Diffusion: Diffusion is the net movement of the molecules of a substance from a region where they are more concentrated to a region where they are less concentrated, arising from the continuous random motion of the molecules, until they become uniformly distributed.

(b) Why diffusion is faster in gases than in liquids (at the same temperature): In a gas the molecules are much farther apart and the intermolecular forces are very weak, so the molecules move freely at high speeds over large distances between collisions. In a liquid the molecules are close together with strong intermolecular forces, so their movement is slower and more restricted. Hence, at the same temperature, molecules of a gas diffuse much faster than those of a liquid.

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(a) Difference between plane polarized light and ordinary light: In ordinary (unpolarized) light the vibrations of the electric field take place in all directions (all planes) perpendicular to the direction of propagation. In plane polarized light the vibrations are restricted to a single plane containing the direction of propagation.

(b) Two uses of polaroids:

1. In polaroid sunglasses, to reduce glare from light reflected off surfaces such as water and roads.
2. In the control of light intensity and in photography (polarizing filters), and in liquid-crystal displays (LCDs) and stress analysis of transparent materials.

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(a) A vector quantity is a physical quantity which has both magnitude and direction. Examples include velocity, force and displacement.

(b)(i) Vector diagram

(b)(ii) Resultant of the vectors

Take east as the positive x-direction and north as the positive y-direction.

Vector	x-component / m s-1	y-component / m s-1
3 m s-1, N45°W	\(-3\sin45^\circ=-2.12\)	\(+3\cos45^\circ=+2.12\)
12 m s-1, W	\(-12.00\)	\(0\)
5 m s-1, S	\(0\)	\(-5.00\)
Resultant components	\(-14.12\)	\(-2.88\)

\[R=\sqrt{(-14.12)^2+(-2.88)^2}=14.4\ \text{m s}^{-1}\]

\[\theta=\tan^{-1}\left(\frac{2.88}{14.12}\right)=11.5^\circ\]

Hence, the resultant is \(14.4\ \text{m s}^{-1}\), \(11.5^\circ\) south of west, or equivalently S78.5°W.

(c)(i) Completed table

Since \(W=Mg\), with \(g=10\ \text{m s}^{-2}\):

Mass, \(M\) / g	Weight, \(W\) / N	Extension, \(e\) / cm
50	0.5	6.5
100	1.0	11.0
150	1.5	15.0
200	2.0	20.0
250	2.5	25.0

(c)(ii) Graph of weight against extension

(c)(iii) The force constant, \(k\), is the gradient of the graph:

Using two widely separated points on the line of best fit, \((10.0\ \text{cm},0.903\ \text{N})\) and \((25.0\ \text{cm},2.530\ \text{N})\),

\[k=\frac{\Delta W}{\Delta e}=\frac{2.530-0.903}{25.0-10.0}=0.1085\ \text{N cm}^{-1}\]

\[k=0.1085\times100=10.85\ \text{N m}^{-1}\approx \boxed{10.8\ \text{N m}^{-1}}\]

(c)(iv) At a mass of 250 g, the extension is 25.0 cm. Therefore,

\[\text{natural length}=38.0-25.0=\boxed{13.0\ \text{cm}}\]

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(a) Mutual induction is the production of an e.m.f. in one coil or circuit when the current in a nearby coil or circuit is changing. The changing current produces a changing magnetic flux which links the second coil.

(b) Uses of electromagnets

1. Electric bells.
2. Electromagnetic relays and switches.
3. Electromagnetic cranes for lifting iron and steel.
4. Magnetic separation of iron scraps from non-magnetic materials.

(c)

1. The alternating current in coil X produces a continuously changing magnetic flux. Some of this flux links coil Y and induces an alternating e.m.f. in it. A current therefore flows through the lamp and it lights.
2. When the coils are brought closer, more of the magnetic flux from X links coil Y. The induced e.m.f. and current in Y increase, so the lamp becomes brighter.
3. The bundle of insulated soft-iron wires has high magnetic permeability and provides a path that concentrates the magnetic flux through both coils. The flux linkage and induced e.m.f. in Y increase, producing a larger current and a brighter lamp. The wires are insulated to reduce eddy currents.

(d)(i) Circuit diagram

(d)(ii) Current through the \(5\,\Omega\) resistor

Since the two cells have equal e.m.f.s and are connected in parallel, the resultant e.m.f. is

\[E = 2.0\text{ V}\]

The equivalent internal resistance is

\[ \frac{1}{r}=\frac{1}{0.4}+\frac{1}{0.1}=2.5+10=12.5 \]

\[ r=\frac{1}{12.5}=0.08\,\Omega \]

Total resistance of the circuit:

\[ R_{\text{total}}=5.0+0.08=5.08\,\Omega \]

Hence,

\[ I=\frac{E}{R_{\text{total}}}=\frac{2.0}{5.08}=0.394\text{ A} \]

Current through the \(5\,\Omega\) resistor \(=0.39\text{ A}\) (approximately).

Akọwa Nkọwa

(a)(i) Two advantages of alcohol over mercury as a thermometric liquid: (1) Alcohol has a much lower freezing point (about -115 °C), so it can measure very low temperatures where mercury would freeze; (2) Alcohol expands more (larger expansivity) for a given temperature rise, making the thermometer more sensitive. (It is also cheaper and can be coloured for easy reading.)

(a)(ii) Mercury level first falls then rises: When the bulb is placed in hot water, the glass bulb is heated first and expands before the heat reaches the mercury. The expansion of the bulb increases the space available, so the mercury level first falls. Shortly afterwards the heat reaches the mercury, which expands much more than the glass, and the level then rises steadily.

(b) Two factors (other than temperature) affecting the rate of evaporation: (1) Surface area exposed; (2) Draught/movement of air over the surface. (Humidity of the surrounding air and nature of the liquid are also acceptable.)

(c) Heating the lead:

(i) Heat to raise the lead to its melting point:

\[ Q = mc\,\Delta\theta = 100\times120\times(320-40) = 100\times120\times280 = 3.36\times10^{6}\,\text{J}. \]

(ii) Additional heat to melt the lead:

\[ Q = mL = 100\times2.5\times10^{4} = 2.5\times10^{6}\,\text{J}. \]

(iii) Time to supply this additional energy (furnace power \(P = 10\,\text{kW} = 10000\,\text{W}\)):

\[ t = \frac{Q}{P} = \frac{2.5\times10^{6}}{10000} = 250\,\text{s}. \]

(d) Two precautions in determining specific latent heat of vaporization of water: (1) Lag (insulate) the apparatus to minimise heat loss to the surroundings; (2) Ensure steady conditions and collect the condensed water only after the water has been boiling steadily (take readings at constant rate). (Correcting for heat losses by repeating at two heating rates is also acceptable.)

Akọwa Nkọwa

By Heisenberg's uncertainty principle for energy and time,

\[ \Delta E \,\Delta t \geq \frac{h}{2\pi} = \hbar. \]

Taking the limiting (minimum) case, the uncertainty in energy is

\[ \Delta E = \frac{\hbar}{\Delta t} = \frac{1.054\times10^{-34}}{2.0\times10^{-9}}. \]

\[ \Delta E = 5.27\times10^{-26}\,\text{J}. \]

The uncertainty in determining the energy of that level is about \(5.27\times10^{-26}\,\text{J}\).

Akọwa Nkọwa

(a) Two applications of electrolysis in industry:

1. Electroplating - coating objects with a thin layer of metal (for example chromium, silver or gold plating) to protect them from corrosion or to improve appearance.
2. Extraction and purification (refining) of metals - such as the extraction of aluminium from molten alumina and the purification of copper by electrolytic refining. (Electrolytic production of chemicals such as caustic soda and chlorine is also acceptable.)

(b) One application of electrolysis in a school laboratory: Electrolysis of acidified water to prepare and collect hydrogen and oxygen gases (for example in a Hofmann voltameter). (Electroplating of a small object or determining the chemical equivalent of a metal are also acceptable.)

Akọwa Nkọwa

The energy gained by a charge \(Q\) accelerated through a potential difference \(V\) is the work done on it:

\[ E = QV. \]

Substituting \(Q = 1.60\times10^{-19}\,\text{C}\) and \(V = 1.0\times10^{5}\,\text{V}\):

\[ E = (1.60\times10^{-19})\times(1.0\times10^{5}) = 1.60\times10^{-14}\,\text{J}. \]

The energy of the electron is \(1.60\times10^{-14}\,\text{J}\).