WAEC SSCE - Physics - 1993

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Longitudinal waves are a type of mechanical waves where the vibrations of the particles are parallel to the direction of wave propagation. These waves can undergo reflection, diffraction, and superposition with other waves. However, longitudinal waves cannot be polarized, which means their vibrations cannot be restricted to a single plane. This is because the particles in the wave are oscillating back and forth in the same direction as the wave is traveling, so there is no way to restrict their motion to a single plane. Therefore, the answer is polarized.

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To solve this problem, we can use the formula: Q = mcΔT Where Q is the heat energy required, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. We can calculate Q as follows: Q = (1 kg) x (4200 J/kg K) x (70°C - 40°C) Q = 126,000 J We can then use the formula: P = Q/t Where P is the power of the heater in watts and t is the time taken to heat the water. Rearranging this formula to solve for t, we get: t = Q/P Substituting the values we know, we get: t = (126,000 J) / (750 W) t = 168 seconds Therefore, it will take the 750 W heater operating at full rating 168 seconds to raise the temperature of 1 kg of water from 40°C to 70°C. The answer is (c) 168s.

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Charging a gold-leaf electroscope by induction involves the following steps: 1. Bringing a charged object (in this case, a negatively charged ebonite rod) close to the cap of the electroscope. This causes the electrons in the cap to be repelled and move to the leaves, which causes them to separate. 2. Earthing the cap. This involves touching the cap of the electroscope with a finger or a conducting wire, which allows the excess charge to flow to the ground. This leaves the electroscope with a temporary charge imbalance. 3. Disconnecting the earthing. This involves removing the finger or conducting wire from the cap of the electroscope, which breaks the connection to the ground. 4. Removing the charged object (the negatively charged ebonite rod). Therefore, the correct sequence of steps for charging a gold-leaf electroscope by induction is: II (bringing a negatively charged ebonite rod close to the cap), III (earthing the cap), IV (disconnecting the earthing), and I (removing the ebonite rod). The answer is option (II, III, IV and I).

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This question relates to the effect of temperature on the volume of a gas. According to Charles's law, at constant pressure, the volume of a gas is directly proportional to its absolute temperature. This means that as the temperature of a gas increases, its volume increases proportionally, and vice versa. In this question, the initial volume of the gas is given as 546 cm³ at O^oC, which is 273K. The final temperature is given as -100^oC, which is 173K. Since the pressure of the gas remains constant, we can use the formula V1/T1 = V2/T2 to find the final volume (V2) of the gas at the new temperature. Substituting the given values in the formula, we have: V1/T1 = V2/T2 546/273 = V2/173 Cross-multiplying, we get: V2 = 546 x 173/273 = 346 cm³ Therefore, the final volume of the gas at -100^oC, assuming constant pressure, is 346 cm³. Hence, the correct option is: 346 cm³.

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The formula for distance traveled by a body with uniform acceleration is given by: distance = (1/2) × acceleration × time² Given that the body starts from rest (initial velocity = 0), and the acceleration is 2ms⁻², and the time taken is 4 seconds, we can substitute these values in the above formula and get: distance = (1/2) × 2ms⁻² × (4 s)² = 16 m Therefore, the distance moved by the body in 4 seconds is 16 meters. Hence, the answer is option (iii) 16m.

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The instantaneous power P in a purely resistive AC circuit is given by the formula P = VI, where V is the voltage and I is the current in the circuit. In this case, we have I = I_o sin wt and V = V_o sin wt, so we can substitute these values into the formula to get: P = VI = (I_o sin wt) (V_o sin wt) Expanding this equation, we get: P = I_o V_o sin²wt Therefore, the answer is (d) I_o V_o sin²wt.

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When an object is projected at an angle to the vertical, it moves in a curved path called a projectile motion. The horizontal and vertical motions of the projectile are independent of each other. The time of flight is the total time taken by the projectile to reach the maximum height and return to the ground level. Let's denote θ as the angle of projection. We can use the following equations to solve for θ: Time of flight = 2usinθ/g where u is the initial velocity and g is the acceleration due to gravity. In this case, u = 100 ms^-1 and the time of flight = 10 s. Therefore, 10 = 2 x 100 x sinθ / 10 Simplifying, we get sinθ = 0.5 To find θ, we take the inverse sine (sin^-1) of 0.5, which gives us θ = 30°. Therefore, the answer is θ = 30°.

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An electric motor primarily converts electrical energy into mechanical energy. An electric motor is a device that works on the principle of electromagnetic induction. When an electric current is passed through a coil of wire that is placed in a magnetic field, a force is generated on the wire, causing it to rotate. This rotational motion is then used to power various machines and devices, such as fans, pumps, and machinery. Thus, an electric motor converts electrical energy into mechanical energy, which can be used for various applications.

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The weight of the block is given by the formula: Weight = Volume x Density x g where g is the acceleration due to gravity. Therefore, the weight of the block is: Weight = (2 x 10^-5 m^3) x (2.5 x 10^-3 kg/m^3) x (10 m/s^2) = 5 x 10^-4 N When the block is half-immersed in water, the upthrust on the block is equal to the weight of the water displaced. The volume of water displaced is half the volume of the block, so the weight of the water displaced is: Weight of water = Volume of water x Density of water x g = (1 x 10^-5 m^3) x (1.0 x 10^3 kg/m^3) x (10 m/s^2) = 0.1 N The reading on the spring balance is equal to the weight of the block minus the weight of the water displaced, so: Reading = Weight - Weight of water = (5 x 10^-4 N) - (0.1 N) = 0.4 N Therefore, the reading on the spring balance is 0.40N.

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Gamma rays are emitted from a radioactive substance without altering either the nucleon number or the proton number of the substance. This means that gamma rays do not affect the atomic structure of the substance, but rather carry energy away from the nucleus. In contrast, alpha and beta particles are emitted during radioactive decay and do change the composition of the nucleus by altering the nucleon and/or proton numbers. Protons and neutrons are subatomic particles that make up the nucleus of an atom and are not typically emitted during radioactive decay. Therefore, the correct answer is gamma rays.

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A Gold-leaf electroscope can be used to compare the relative magnitude of similar charges on two given bodies. A Gold-leaf electroscope is an instrument that detects the presence of an electric charge by using two thin gold leaves that are suspended from a conducting rod. When a charged object is brought near the electroscope, the leaves are repelled due to the electrostatic force of the charge. The amount of separation of the leaves gives an indication of the magnitude of the charge on the object. By comparing the amount of separation of the leaves with two different charged objects, it is possible to determine the relative magnitude of the charges on the objects.

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The phenomenon of radioactivity was first discovered by Henn Becquerel. In 1896, Becquerel discovered that a uranium compound placed near a photographic plate caused the plate to darken. This phenomenon occurred even when the uranium compound was not exposed to light, suggesting that it was emitting a type of radiation that could penetrate through solid objects. Becquerel's discovery paved the way for further research into radioactivity, which eventually led to the development of nuclear physics and its applications.

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When an atom is in the ground state, it means that all its electrons are in their lowest energy levels, which are also called their stable energy levels. In this state, the atom is said to be in its most stable and lowest energy state, and is less likely to undergo any chemical or nuclear reactions. When an atom absorbs energy, its electrons can move to higher energy levels, and the atom is then said to be in an excited state. Atoms in excited states are generally more reactive and can undergo chemical or nuclear reactions. Therefore, the correct answer to the question is "stable."

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Out of the given options, "mass" is not an example of a force. Mass is a measure of the amount of matter present in an object, and it is measured in kilograms or grams. On the other hand, force is a physical quantity that changes or tends to change the state of rest or motion of an object. It is measured in newtons (N). Therefore, the correct answer is "Mass."

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To calculate the mean period of oscillation, we need to find the time taken for one oscillation (the period) for each of the three trials, and then take the average. Let's start by calculating the time taken for one oscillation for each trial. For the first trial, the time taken for 20 oscillations is 44.3 s, so the time taken for one oscillation is: Time for 1 oscillation = 44.3 s ÷ 20 = 2.215 s Similarly, for the second trial: Time for 1 oscillation = 45.5 s ÷ 20 = 2.275 s And for the third trial: Time for 1 oscillation = 45.7 s ÷ 20 = 2.285 s Now, we can calculate the mean period of oscillation by taking the average of these three values: Mean period of oscillation = (2.215 s + 2.275 s + 2.285 s) ÷ 3 ≈ 2.26 s Therefore, the mean period of oscillation of the pendulum is approximately 2.26 s. The correct answer is 2.26s.

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The unit of inductance is henry. Inductance is a property of an electrical circuit that opposes any change in current flowing through it. It is defined as the ratio of the magnetic flux through a circuit to the current flowing in the circuit. The unit is named after Joseph Henry, an American scientist who discovered electromagnetic induction independently of Michael Faraday. The symbol for inductance is H, and one henry is defined as the amount of inductance that will produce an electromotive force of one volt when the current through the inductor changes at a rate of one ampere per second.

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Out of the given options, the percussion instrument is a bell. A percussion instrument is any musical instrument that produces sound through striking, shaking or scraping. Bells are struck to produce sound, thus making them a percussion instrument. Flute, organ, piano, and sonometer are not percussion instruments, as they produce sound through blowing, pressing keys, or plucking strings.

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Radio waves have the longest wavelengths among the given options. This is because radio waves have the lowest frequency and the longest wavelength in the electromagnetic spectrum, ranging from about 1 millimeter to over 100 kilometers. They are commonly used for communication purposes, such as radio and television broadcasts, cell phone signals, and Wi-Fi. Infra-red, ultra-violet, X-rays, and gamma rays have shorter wavelengths and higher frequencies than radio waves, and are used in various applications such as medical imaging, sterilization, and remote sensing.

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The force experienced by a charged particle moving in a magnetic field is given by the formula F = Bqv, where B is the magnetic field strength, q is the charge of the particle, and v is the velocity of the particle. In this case, the charge on the particle is 5C, the magnetic field strength is 0.01T, and the velocity of the particle is 1.5ms^-1. Thus, substituting the given values into the formula, we get: F = (0.01T)(5C)(1.5ms^-1) = 0.075N Therefore, the magnitude of the force exerted on the particle is 0.075N. So, the correct option is (b) 0.075N.

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The initial atom of Uranium-238 emits eight alpha particles (helium-4 nuclei) and B beta particles (electrons or positrons) in order to reach stability. An alpha particle contains two protons and two neutrons, so the emission of one alpha particle reduces the nucleon number by 4. Thus, the total reduction in nucleon number due to the emission of eight alpha particles is 8 x 4 = 32. A beta particle, on the other hand, has negligible mass and does not affect the nucleon number of the atom. Therefore, the nucleon number of the final product in the chain reaction can be calculated by subtracting the total reduction in nucleon number (32) from the original nucleon number of 238. 238 - 32 = 206 Hence, the nucleon number of the final product is 206. Therefore, the correct option is (a) 206.

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Electrical resistance is a measure of how much a material opposes the flow of electric current. When an electric current flows through a conductor, some of the electrical energy is converted into heat energy due to collisions between electrons and the atoms of the conductor. This conversion of electrical energy into heat energy is the result of electrical resistance. Therefore, the correct answer is "heat energy".

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The correct expression that expresses the magnitude of the electric field intensity between two points A and B situated at a distance d apart is, which is Vd^-1. The electric field intensity is defined as the amount of electric force acting per unit charge. The potential difference between two points is defined as the work done per unit charge in moving a positive charge from one point to another. Hence, the electric field intensity E between the two points A and B can be obtained by dividing the potential difference V by the distance d between the two points. Therefore, E = V/d, which is equivalent to Vd^-1.

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When a sound wave travels and hits a surface, it reflects back as an echo. The time taken for the echo to return to the source is twice the time taken for the sound to travel from the source to the reflecting surface. Let's call the distance between the man and the wall "x". The sound travels the distance "x" to the wall and then reflects back to the man another distance "x". So, the total distance traveled by the sound is 2x. We know that the speed of sound in air is 330ms^-1. Using the formula, distance = speed x time we can write the equation as follows: 2x = 330 x 2 Simplifying this equation, we get: 2x = 660 Dividing both sides by 2, we get: x = 330 Therefore, the distance between the man and the wall is 330 meters. So the correct answer is: 330m.

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When an object moves in a circle, it is constantly changing its direction, which means that it is accelerating. This is because acceleration is the rate of change of velocity, and velocity is a vector that includes both speed and direction. In this case, the object is moving with a uniform angular speed, which means that it is moving at a constant speed in a circle. The formula for acceleration towards the center of a circle is given by a = v^2 / r, where v is the speed of the object and r is the radius of the circle. We know that the speed of the object is 3.0 m/s, and we are given the angular speed of the object as 0.6 rad/s. Angular speed is the rate at which the object moves around the circle in radians per second. To find the radius of the circle, we need to use the relationship between angular speed, linear speed, and radius, which is given by v = ωr, where ω is the angular speed. Rearranging this formula gives us r = v/ω. Substituting the values we have, we get r = 3.0 m/s / 0.6 rad/s = 5.0 m. Now we can calculate the acceleration towards the center of the circle using the formula a = v^2 / r. Substituting the values we have, we get a = (3.0 m/s)^2 / 5.0 m = 1.8 m/s^2. Therefore, the answer is option D: 1.8 ms^-2.

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The electric field strength is defined as the force experienced by a unit charge in an electric field. Mathematically, the electric field strength (E) is given by: E = F / q where F is the force experienced by the charge and q is the magnitude of the charge. In this question, we are given the force (F) experienced by a point charge of 1.0 x 10^-7 C in a uniform electric field. The force is 0.01 N. Therefore, we can calculate the electric field strength as: E = F / q E = 0.01 / 1.0 x 10^-7 E = 1.0 x 10^5 Vm^-1 Therefore, the magnitude of the strength of the electric field is 1.0 x 10^5 Vm^-1. The correct option is (b).

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Gamma rays have the greatest penetrating power. This is because they have high energy and no charge, which allows them to penetrate most materials with ease. Alpha particles, on the other hand, have the least penetrating power due to their large size and positive charge. Beta particles and electrons have moderate penetrating power, while neutrons have low to moderate penetrating power depending on their energy level.

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Light and sound waves are both associated with energy transfer, but they differ in many other aspects. Sound waves are mechanical waves that require a material medium to propagate, such as air, water, or solids. In contrast, light waves are electromagnetic waves that can propagate through vacuum and do not require a material medium. Sound waves are longitudinal waves, which means that the particles of the medium vibrate parallel to the direction of the wave propagation. On the other hand, light waves are transverse waves, which means that the electric and magnetic fields oscillate perpendicular to the direction of the wave propagation. The velocity of sound waves depends on the medium through which they propagate, and it is generally much slower than the velocity of light in vacuum. For instance, the velocity of sound in air at room temperature is about 330 m/s, while the velocity of light in vacuum is approximately 3 x 10^8 m/s. Finally, only light waves can be polarized, meaning that their oscillations can be confined to a particular plane. Sound waves cannot be polarized.

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A derived unit is a unit that is obtained by combining base units. Base units are the fundamental units of measurement that are defined by standards and are used to measure physical quantities such as length, mass, time, electric current, temperature, and amount of substance. Out of the options given, Ohm is the only derived unit. It is derived from the base units of length, mass, and time, and is used to measure electrical resistance. Ampere is the base unit of electric current, kilogramme is the base unit of mass, second is the base unit of time, and Kelvin is the base unit of temperature.

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We can solve this problem by first finding the amount of heat energy required to melt the ice and then using that to calculate the current passing through the coil. The amount of heat energy required to melt the ice is given by: Q = mL where Q is the amount of heat energy, m is the mass of the ice, and L is the latent heat of fusion of ice. Substituting the given values, we get: Q = 10g x 336 Jg^-1 = 3360 J Since there are no heat losses, all the electrical energy supplied to the coil is converted into heat energy to melt the ice. The electrical energy supplied is given by: E = VIt where E is the electrical energy, V is the voltage, I is the current, and t is the time taken. Since the voltage is not given, we cannot directly solve for the current. However, we can use the fact that the coil melts the ice in 21 seconds to find the current. Since all the electrical energy supplied is used to melt the ice, we can equate E and Q: VIt = 3360 J Solving for I, we get: I = 3360 J / (Vt) Substituting the given values, we get: I = 3360 J / (10 Ω x 21 s) = 16.00 A Therefore, the amount of current passing through the coil is 16.00 A. Answer: 16.00A

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The equation above represents a nuclear decay of a sodium isotope. In the equation, the left-hand side represents the parent nucleus (24 Na) and the right-hand side represents the daughter nucleus (24 mg4) and the emitted particles. The mass number (24) is conserved on both sides of the equation, but the atomic number (11) on the left side is larger than the atomic number (12) on the right side, indicating that the parent nucleus has undergone beta decay. During beta decay, a neutron in the nucleus is converted into a proton and an electron, which is emitted as a beta particle. Therefore, the X in the equation represents a beta particle.

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The gravitational potential due to a point mass m at a distance r from it is given by the expression: - -Gm/r Here, G is the gravitational constant which has a fixed value, m is the mass of the point source and r is the distance between the point source and the point at which we want to calculate the gravitational potential. The negative sign indicates that the gravitational potential decreases with an increase in distance from the source. This expression is derived from the equation for gravitational potential energy, which is given by: - U = -GmM/r where M is the mass of the object that is being attracted by the point source. The negative sign indicates that the potential energy of the system decreases as the two masses move closer to each other. The gravitational potential is the potential energy per unit mass, so dividing both sides of the above equation by M, we get: - V = U/M = -Gm/r Therefore, the gravitational potential due to a point mass m at a distance r from it is -Gm/r.

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In a parallel circuit, the potential difference across each component is the same. Therefore, each of the three lamps has a potential difference of 250 V across it. Each lamp has a power of 100 W, so the current passing through it is: I = P / V = 100 / 250 = 0.4 A Since the three lamps are in parallel, the total current drawn from the supply is the sum of the current through each lamp: I_total = 0.4 + 0.4 + 0.4 = 1.2 A Therefore, the reading of the ammeter would be 1.2A. Answer: 1.2A

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Glass is not a conductor of electricity. This is because it is a non-metallic material and does not have any free electrons to carry the electric charge. In contrast, metals such as silver and copper are good conductors of electricity because they have a large number of free electrons that can move easily through the material in response to an electric field. The human body can also conduct electricity to some extent, although this can be dangerous depending on the circumstances. The Earth is a complex case - it is a good conductor of electricity in some contexts, such as during a lightning strike, but is not a good conductor in other contexts.

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When two mirrors are inclined at an angle, the number of images formed is given by the formula n = 360°/θ - 1, where n is the number of images and θ is the angle between the mirrors. In this case, the angle between the two mirrors is 120°. Substituting in the formula we have, n = 360°/120° - 1 = 3 - 1 = 2. Therefore, two images will be observed in the two mirrors.

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A diverging lens, also known as a concave lens, is a lens that is thinnest at its center and thicker towards its edges. This type of lens always forms an image that is virtual, upright, and diminished. A virtual image is an image that cannot be projected onto a screen and is located behind the lens. An upright image is one that appears in the same orientation as the object being viewed. A diminished image is one that is smaller than the object being viewed. Therefore, the correct answer is "diminished, virtual and erect".

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In a series R-C circuit, the total impedance (Z) is given by the square root of the sum of the squares of the resistance (R) and reactance (X). Mathematically, we can represent this as Z = sqrt(R^2 + X^2). In this case, R = 4Ω and Xc = 3Ω. Since the capacitor has a negative reactance, we can write Xc as -1/ωC, where ω is the angular frequency of the circuit and C is the capacitance of the capacitor. However, since we are not given the frequency or capacitance in the question, we cannot calculate the exact value of Xc. Therefore, we will assume that Xc = -3Ω, which means that the capacitive reactance cancels out part of the resistance. Now, we can use the formula for impedance to calculate the total impedance of the circuit as follows: Z = sqrt(R^2 + Xc^2) Z = sqrt(4^2 + (-3)^2) Z = sqrt(16 + 9) Z = sqrt(25) Z = 5Ω Therefore, the impedance of the circuit is 5Ω.

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The purpose of a short chain attached to the back of a petrol tanker and trailing behind it is to ensure that any charges generated by friction in the tanker are conducted to the earth. This is done to prevent any static electricity buildup, which could potentially lead to dangerous sparks or even explosions when the petrol is being pumped or transferred. The chain provides a path for any static charges to dissipate harmlessly into the earth, minimizing the risk of accidents.

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An image which cannot be formed on a screen is said to be a virtual image. A virtual image is formed when light rays diverge after reflection or refraction and they do not actually pass through the position of the image. Therefore, the image cannot be projected onto a screen or captured on a surface. Virtual images are always erect and cannot be focused. Examples of virtual images are the images formed by a plane mirror or a convex lens when the object is placed inside the focal point.

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The formula to calculate the distance covered by an object with constant acceleration is: distance = (initial velocity * time) + (0.5 * acceleration * time^2) Here, the particle starts from rest, which means its initial velocity (u) is 0. The acceleration (a) is given as 0.5 ms^-2, and the distance covered (s) is 25m. So we can rewrite the formula as: 25m = (0 * t) + (0.5 * 0.5 ms^-2 * t^2) Simplifying: 25m = 0.25 * t^2 t^2 = 100 t = sqrt(100) = 10s Therefore, the time taken by the particle to cover a distance of 25m is 10 seconds. Hence, the correct answer is 10.0s.

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When two objects collide, the total momentum before the collision is equal to the total momentum after the collision. That is, the momentum is conserved. Therefore, we can write: M₁U = (M₁ + M₂)V Solving for V, we get: V = (M₁U)/(M₁ + M₂) So the correct expression for V is:

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The function of manganese (IV) oxide in a Leclanche cell is to prevent polarization in the cell. When a Leclanche cell discharges, the zinc electrode releases electrons to the anode, forming zinc ions and releasing hydrogen ions in the electrolyte. As more and more hydrogen ions are produced, the concentration of hydrogen ions increases, and the cell's voltage drops, leading to a phenomenon known as polarization. Manganese (IV) oxide acts as a depolarizer, which reacts with the hydrogen ions in the electrolyte to produce water and prevent the accumulation of hydrogen ions. This helps to maintain the voltage of the cell and prevent polarization. Therefore, option C, "prevent polarization in the cell," is the correct answer.

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To calculate the cost of operating the refrigerator for 30 days, we need to determine the total energy consumed by the refrigerator in that time period. The energy consumed by an electrical appliance is given by the product of its power and the time for which it is operated. Here, the power of the refrigerator is 200 W, and the time for which it is operated is 30 days. However, we need to convert the time to hours since the power is given in watts, which is a unit of power per unit time, usually measured in seconds. One day has 24 hours, so 30 days have 30 x 24 = 720 hours. Therefore, the total energy consumed by the refrigerator in 30 days is: Energy = Power x Time Energy = 200 W x 720 hours Energy = 144000 Wh We now need to convert this energy to kilowatt-hours (kWh) since the cost of electricity is given in k per kWh. To do this, we divide the energy by 1000: Energy = 144000 Wh = 144 kWh The cost of electricity is 5 k per kWh, so the cost of operating the refrigerator for 30 days is: Cost = Energy x Cost per kWh Cost = 144 kWh x 5 k/kWh Cost = 720 kobo or N7.20 Therefore, the correct answer is option A) N7.20.

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In the normal use of a simple microscope, a person sees an erect, virtual and magnified image. When the object is placed below the focus point of the lens, the lens produces an enlarged virtual image that is upright, meaning it is not inverted. The image is virtual, which means it appears to be at a position where light rays do not actually converge. Finally, the image is magnified, meaning it appears larger than the actual size of the object.

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(a) Experiment

A uniform capillary tube is sealed at one end. A short pellet of mercury traps a fixed mass of dry air between the sealed end and the mercury pellet. The tube is held horizontally in a stirred water bath beside a half-metre rule, with a thermometer in the bath. The mercury pellet is free to move, and the pressure on its outer face remains constant.

At a steady temperature \(\theta\), read the temperature from the thermometer and the length \(L\) of the trapped air column from the rule. Heat the water bath slowly, stirring continuously, and repeat the readings at several steady temperatures. Since the capillary tube has a uniform bore, \(V\propto L\).

Temperature, \(\theta\) (°C)	0	20	40	60	80	100
Length, \(L\) (cm)	13.7	14.7	15.7	16.7	17.7	18.7

A plot of \(L\) against \(\theta\) is a straight line. When produced backwards, it cuts the temperature axis at about \(-274\ ^\circ\mathrm{C}\). Thus, for a fixed mass of air at constant pressure, its volume increases uniformly with temperature.

Precautions: Use dry air; stir the water to maintain a uniform temperature; take readings only when the temperature is steady; and avoid parallax when reading the thermometer and rule.

(b) Since the tube is uniform, \(V\propto L\). Therefore, the cubical expansivity is

\[\gamma=\frac{V_{100}-V_0}{V_0(100-0)}=\frac{L_{100}-L_0}{L_0\times100}\]

\[\gamma=\frac{18.7-13.7}{13.7\times100}=\frac{5.0}{1370}=3.65\times10^{-3}\ \mathrm{K^{-1}}.\]

(c) Increasing the temperature increases the average kinetic energy and speed of the gas molecules. The molecules would then strike the walls more forcefully and tend to increase the pressure. At constant pressure, the gas expands so that the molecules travel greater distances between collisions with the walls. Hence the volume of the fixed mass of gas increases.

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(a) Laws of electromagnetic induction

1. Whenever the magnetic flux linking a conductor or coil changes, an e.m.f. is induced in it. The magnitude of the induced e.m.f. is proportional to the rate of change of flux linkage:
   \[E=-N\frac{d\Phi}{dt}.\]
2. The induced current flows in such a direction as to oppose the change in magnetic flux that produces it. This is Lenz's law.

(b) Labelled diagram of a simple d.c. generator

How it works: A rectangular coil is rotated mechanically between the poles of a magnet. As the coil rotates, the magnetic flux linking it changes and an e.m.f. is induced in the coil. The induced e.m.f. in the coil reverses after every half revolution. However, at the same instant, the split-ring commutator reverses contact with the carbon brushes. Thus, the connections to the external circuit are reversed whenever the coil current reverses, so current in the external circuit always flows in one direction. The output is therefore a pulsating direct current.

(c) Three methods of obtaining a higher e.m.f.

1. Increase the number of turns of wire in the coil.
2. Use a stronger magnetic field, for example by using stronger magnets or a soft-iron core.
3. Rotate the coil faster.

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(a)(i) Nuclear fusion: the joining together of two light atomic nuclei to form a single heavier nucleus, with the release of a large amount of energy. Example: the fusion of hydrogen (deuterium) nuclei to form helium in the Sun.

(a)(ii) Nuclear fission: the splitting of a heavy atomic nucleus into two lighter nuclei of comparable mass, accompanied by the release of neutrons and a large amount of energy. Example: the splitting of a uranium-235 nucleus when it captures a slow neutron.

(a)(iii) Radiation hazards: the harmful effects that nuclear radiations (alpha, beta, gamma) have on living tissue. Example: exposure to gamma rays can damage or kill body cells and cause cancer or genetic mutations.

(b) Two advantages of fusion over fission:

• Fusion produces more energy per unit mass of fuel and its fuel (hydrogen) is cheap and abundant.
• Fusion produces little or no long-lived radioactive waste, so it is cleaner.

In spite of these, fusion is not normally used for power generation because it requires extremely high temperatures (millions of degrees) and pressures to bring the nuclei close enough to fuse, and no ordinary container can withstand or confine such conditions economically.

(c) Given \(I=30\sin100\pi t\), compare with \(I=I_o\sin(2\pi f t)\).

(i) Frequency: \(2\pi f=100\pi\Rightarrow f=50\,\text{Hz}\).

(ii) Peak value: \(I_o=30\,\text{A}\).

(iii) r.m.s. value: \(I_{rms}=\dfrac{I_o}{\sqrt{2}}=\dfrac{30}{\sqrt{2}}=21.2\,\text{A}\).

Maelezo ya Majibu

(a)(i) A machine is a device by means of which a force (the effort) applied at one point is used to overcome another force (the load) at some other point, usually giving a mechanical advantage or a change in the direction of the force.

(a)(ii)

• Mechanical advantage (M.A.) is the ratio of the load to the effort: \(M.A.=\dfrac{L}{E}\).
• Velocity ratio (V.R.) is the ratio of the distance moved by the effort to the distance moved by the load in the same time: \(V.R.=\dfrac{\text{effort distance}}{\text{load distance}}\).
• Efficiency is the ratio of the useful work output to the work input, expressed as a percentage.

Derivation. \(\text{Efficiency}=\dfrac{\text{work output}}{\text{work input}}=\dfrac{L\times d_L}{E\times d_E}=\dfrac{L/E}{d_E/d_L}=\dfrac{M.A.}{V.R.}\). Hence \(\text{Efficiency}=\dfrac{M.A.}{V.R.}\times100\%\).

(b) Efficiency is less than 100% because part of the work input is used to overcome friction between moving parts and to lift the useless (movable) parts of the machine; this energy is lost mainly as heat and is not delivered to the load.

(c) Pitch = 4.4 mm = \(4.4\times10^{-3}\,\text{m}\); tommy bar L = 70 cm = 0.70 m; height h = 20 cm = 0.20 m; mass = 8000 kg.

(i) Velocity ratio: \(V.R.=\dfrac{2\pi L}{\text{pitch}}=\dfrac{2\times\frac{22}{7}\times0.70}{4.4\times10^{-3}}=\dfrac{4.4}{4.4\times10^{-3}}=1000\).

(ii) Mechanical advantage: \(M.A.=\text{efficiency}\times V.R.=0.80\times1000=800\).

(iii) Effort: Load \(=mg=8000\times10=80000\,\text{N}\). \(E=\dfrac{L}{M.A.}=\dfrac{80000}{800}=100\,\text{N}\).

(iv) Work done by the effort: \(=\dfrac{\text{work output}}{\text{efficiency}}=\dfrac{mgh}{0.80}=\dfrac{80000\times0.20}{0.80}=\dfrac{16000}{0.80}=20000\,\text{J}=20\,\text{kJ}\).