WAEC SSCE - Physics - 1988

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The instrument that may be used to measure the relative humidity is the hygrometer. Relative humidity is the amount of moisture in the air compared to the maximum amount that the air could hold at a given temperature. It is expressed as a percentage. To measure relative humidity, we need an instrument that can measure the amount of moisture in the air. A hygrometer is a device that is specifically designed to measure humidity. There are different types of hygrometers, but they all work based on the principle of measuring the change in some physical property of a substance in response to changes in humidity. For example, a common type of hygrometer is the hair hygrometer, which measures humidity by monitoring the length of a human hair. Hair expands as humidity increases and contracts as humidity decreases. The length of the hair is measured with a scale or a magnifying glass, and the relative humidity is determined from a calibration chart. Another type of hygrometer is the electronic hygrometer, which uses a humidity sensor to measure the moisture content of the air. The sensor consists of a thin film of material that changes its electrical properties in response to changes in humidity. The change in electrical resistance, capacitance, or voltage can be measured and used to determine the relative humidity. In contrast, a hydrometer is a device that is used to measure the density of a liquid. A barometer measures atmospheric pressure, a manometer measures the pressure of a gas or liquid, and a hypsometer measures altitude. Therefore, the correct instrument that may be used to measure relative humidity is the hygrometer.

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Neutrons are not affected by a magnetic field because they have no electrical charge. Cathode rays and Alpha particles are charged and can be deflected by a magnetic field. Therefore, the answer is (I) only.

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The correct relationship between linear speed V and angular speed ω of a body moving uniformly in a circle of radius r is, V = ωr. This equation means that the linear speed of an object moving in a circle is directly proportional to its angular speed and the radius of the circle. In other words, the larger the angular speed or the radius of the circle, the faster the object moves in a linear path. To understand this relationship, consider a point on a rotating wheel of radius r. As the wheel rotates, the point moves in a circle of circumference 2πr with an angular speed ω. If the point completes one full revolution in a time of T seconds, then its angular speed is ω = 2π/T. The linear speed V of the point is the distance it travels in a unit time, which is the circumference of the circle divided by the time taken to complete one revolution. Thus, V = 2πr/T. We can substitute the expression for ω in terms of T in the above equation to get V = ωr, which is the correct relationship between linear speed and angular speed for a body moving uniformly in a circle of radius r.

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The speed of sound is given as 330ms^-1. The relationship between speed, frequency, and wavelength of a wave is given as V = fλ, where V is the speed, f is the frequency, and λ is the wavelength. Solving for frequency (f), we get f = V/λ. Substituting the values given, we have f = 330/1.65 = 200 Hz. The period of vibration is the time it takes for one complete vibration or cycle, and is given as T = 1/f. Substituting the value of frequency obtained above, we have T = 1/200 = 0.005 s. Therefore, the correct answer is 0.005.

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When three coplanar and non-parallel forces are in equilibrium, there are certain properties that hold:
I. The three forces can be represented in magnitude and direction by the three sides of a triangle taken in order. This is known as the triangle of forces.
II. The lines of action of the three forces meet at a point. This point is called the point of concurrency.
III. The magnitude of any one force is equal to the magnitude of the resultant of the other two.
IV. Any one force is the equilibrant of the other two.

Therefore, the correct statements are:
I & II are always true for any three coplanar non-parallel forces in equilibrium.
III is true because the resultant of two forces is equal in magnitude and opposite in direction to the third force.
IV is also true because the equilibrant of two forces is equal in magnitude and opposite in direction to the third force.
Therefore, the correct answer is:
I, II, III & IV.

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The half-life of a radioactive element is the amount of time it takes for half of the initial number of atoms to decay. For element A, the half-life is 100 years, which means that after 100 years, half of the initial number of atoms will have decayed, leaving half remaining. Similarly, for element B, the half-life is 50 years, which means that after 50 years, half of the initial number of atoms will have decayed, leaving half remaining. After 200 years, we can calculate the remaining amount of each element using the following formula: Remaining amount = Initial amount * (1/2)^(time/half-life) For element A, we have: Remaining amount of A = Initial amount of A * (1/2)^(200/100) = (1/2)^2 * Initial amount of A = (1/4) * Initial amount of A For element B, we have: Remaining amount of B = Initial amount of B * (1/2)^(200/50) = (1/2)^4 * Initial amount of B = (1/16) * Initial amount of B Since the initial amounts of A and B are equal, we can compare their remaining amounts by simply dividing one by the other: Remaining amount of A / Remaining amount of B = [(1/4) * Initial amount of A] / [(1/16) * Initial amount of B] = (1/4) / (1/16) = 4 Therefore, the ratio of the number of remaining atoms of A to that of B after 200 years is 4:1. Option A is the correct answer.

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When sound travels to a reflecting surface and then back to the listener, it creates an echo. The distance from the listener to the reflecting surface can be calculated by dividing the total distance traveled by the sound by 2, because sound travels at a constant speed in all directions. Let's assume that the distance from the boy to the cliff is x meters. The sound will travel a distance of 2x meters: x meters from the boy to the cliff, and then x meters from the cliff back to the boy. The time taken for the sound to travel this distance is 0.5 seconds. We can use the formula speed = distance/time to find the speed of sound. Plugging in the values we get: 340 = 2x/0.5 Solving for x, we get: x = (340 x 0.5)/2 = 85 meters Therefore, the boy is standing 85 meters away from the cliff. The answer is option C.

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To calculate the kinetic energy of the electron, we need to use the formula: K.E = qV where q is the charge of the electron and V is the potential difference. Given: q = 1.6 x 10^(-19) C V = 40 kV = 40 x 10^3 V Substituting the values in the formula, we get: K.E = (1.6 x 10^(-19) C) x (40 x 10^3 V) K.E = 6.4 x 10^(-15) J Therefore, the kinetic energy of the electron is 6.4 x 10^(-15) J. Hence the option that corresponds to this answer is: 6.4 x 10^-15 J.

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The correct answer is "average speed". Average speed is the total distance covered by an object over a period of time, whereas average velocity is the displacement of an object over a period of time. Since both the train and the lorry travel the same distance during the same interval, they must have the same average speed. It is important to note that this does not necessarily mean that they have the same average velocity, as their displacements could differ.

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The answer to this question is "Sound waves". Sound waves are not considered as an electromagnetic radiation because they are mechanical waves that require a medium (such as air, water or solids) to travel through, whereas electromagnetic radiation does not require a medium and can travel through a vacuum. The other options - X-ray, radio waves, sunlight and infrared radiation - are all examples of electromagnetic radiation.

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When a man is standing on a bench, the pressure he exerts on the bench depends on the force he applies and the area of contact between his feet and the bench. The greater the force he applies, the greater the pressure he exerts on the bench. Therefore, the option that exerts the greatest pressure on the bench is when the man stands on the toes of one foot, as this reduces the area of contact between the foot and the bench, leading to a higher pressure. This is due to the fact that pressure is defined as force per unit area, so if the area of contact decreases, the pressure increases for a constant force.

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The specific latent heat of fusion of ice is the amount of energy required to change the state of a unit mass of ice from solid to liquid or from liquid to solid without changing its temperature. We can calculate the specific latent heat of fusion of ice by using the formula: Q = mL where Q is the amount of energy transferred, m is the mass of the substance, and L is the specific latent heat of fusion. In this case, we know that 0.5kg of water at 10°C is completely converted to ice by extracting 188000J of heat from it. We also know that the specific heat capacity of water is 4200J kg^-1C^-1. First, we need to calculate the amount of energy required to cool the water from 10°C to 0°C: Q1 = mcΔT where m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Q1 = (0.5kg)(4200J kg^-1C^-1)(10°C) = 21000J Next, we need to calculate the amount of energy required to convert the water at 0°C to ice at 0°C: Q2 = mL where m is the mass of water, and L is the specific latent heat of fusion of ice. Q2 = (0.5kg)(L) We know that the total amount of energy transferred is 188000J. Therefore, we can write: Q1 + Q2 = 188000J Substituting the values of Q1 and Q2, we get: 21000J + (0.5kg)(L) = 188000J Simplifying and solving for L, we get: L = (188000J - 21000J) / 0.5kg L = 334000J kg^-1 Therefore, the specific latent heat of fusion of ice is 334.0 KJ kg^-1. So the answer is: - 334.0 KJ kg^-1.

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The statement that is not correct about radiant heat is option I only, which states that radiant heat cannot travel through a vacuum. In reality, radiant heat can travel through a vacuum. Radiant heat is a type of energy that travels in the form of electromagnetic waves, and it can travel through a vacuum because it doesn't require a medium to propagate. Option II is correct because rough surfaces emit more radiant heat than polished surfaces because they have more surface area and can radiate more efficiently. Option III is also correct because dark surfaces absorb more radiant heat than bright surfaces because they absorb more radiation due to their high emissivity.

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The effect of increased loudness observed when a sounding tuning fork is brought near the end of a pipe containing an air column is due to resonance. Resonance occurs when a vibrating object or sound wave causes another object to vibrate at its natural frequency. In this case, the air column in the pipe has a natural frequency of vibration, which depends on its length and the speed of sound in air. When the tuning fork is brought near the end of the pipe, it emits sound waves of a particular frequency, which can cause the air column to vibrate at its natural frequency. If the length of the air column is adjusted so that it resonates with the frequency of the tuning fork, a large-amplitude vibration is produced, resulting in a loud sound. This is because the energy transferred to the air column by the tuning fork is efficiently transferred to the entire column of air, creating a large-amplitude sound wave. The phenomenon of resonance is used in many musical instruments, such as guitars, pianos, and wind instruments, to amplify the sound produced by the instrument. In summary, the increased loudness observed when a sounding tuning fork is brought near the end of a pipe containing an air column is due to resonance.

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The motion of a body is simple harmonic if the acceleration is directed towards a fixed point and proportional to its distance from the point. In other words, if a body moves back and forth along a straight line or rotates back and forth around a fixed point, and its acceleration is always directed towards a fixed point and proportional to its distance from that point, then the motion of the body is simple harmonic. A simple example of this is the motion of a mass attached to a spring. When the mass is displaced from its equilibrium position and released, it oscillates back and forth, with the acceleration directed towards the equilibrium point and proportional to the distance from that point. This motion is simple harmonic. Another example is the motion of a pendulum. When a pendulum is displaced from its rest position and released, it swings back and forth, with the acceleration directed towards the equilibrium point and proportional to the distance from that point. This motion is also simple harmonic. In summary, the motion of a body is simple harmonic if it oscillates or rotates back and forth around a fixed point, and its acceleration is directed towards that point and proportional to the distance from it.

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The unit of inductance is the henry (H), named after the American scientist Joseph Henry. Inductance is the property of an electrical circuit that opposes changes in current. It is created by a coil of wire that produces a magnetic field when current flows through it. The strength of this magnetic field depends on the number of turns of wire in the coil, the current flowing through the coil, and the material surrounding the coil. The unit of inductance, the henry, is defined as the amount of inductance that produces an electromotive force of one volt when the current in the circuit changes at a rate of one ampere per second. In practical applications, inductance is measured in millihenries (mH) or microhenries (μH). Therefore, the answer is: - Henry.

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The correct option is "Gamma particles". Gamma particles are a type of electromagnetic radiation with the highest frequency and shortest wavelength. Due to their high energy and lack of charge, they can penetrate through materials with the highest density and thickness, such as concrete and lead. Beta particles are fast-moving electrons that can penetrate through thin metal sheets and cause damage to living cells. Alpha particles are helium nuclei and have the largest mass but low penetrating power, being stopped by a sheet of paper or a few centimeters of air. Electrons are negatively charged subatomic particles with moderate penetrating power, and neutrons have no charge and moderate penetrating power, being able to penetrate through materials with low density.

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The units of physical quantities that are derived are those that are not fundamental and can be expressed in terms of the fundamental units. I. Area is derived from the fundamental unit of length, and the unit of area is expressed as square units of length, such as square meters or square centimeters. II. Thrust is derived from the fundamental units of mass, length, and time, and its unit is expressed as newtons, which is equivalent to kg•m/s^2. III. Pressure is derived from the fundamental units of force and area, and its unit is expressed as newtons per square meter, or pascals. IV. Mass is a fundamental quantity, and its unit is expressed as kilograms. Therefore, the units of physical quantities that are derived are I, II, and III only, and the correct answer is (b) I, II, III only.

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The saturation vapour pressure of a liquid is affected by the temperature of the liquid. As the temperature increases, the saturation vapour pressure of the liquid also increases. This is because as the temperature increases, the molecules in the liquid gain more kinetic energy, and some of them escape into the air as vapour. Humidity of air can also affect the saturation vapour pressure of a liquid. If the air is already saturated with water vapour, then the saturation vapour pressure of the liquid will be lower, as there is less room for more water vapour to enter the air. The volume of vapour and the mass of the liquid do not directly affect the saturation vapour pressure of a liquid. However, they can affect the conditions under which the liquid exists, and thus indirectly affect the saturation vapour pressure. The volume of the liquid can affect the surface area of the liquid that is exposed to the air, which can in turn affect the rate at which the liquid evaporates. The volume of vapour can affect the pressure of the surrounding air, which can affect the rate of evaporation of the liquid. In summary, the temperature of the liquid and the humidity of the air are the primary factors that affect the saturation vapour pressure of a liquid.

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The temperature at which the water vapor present in the air is just sufficient to saturate it is called the dew point. The air around us can hold a certain amount of water vapor, which is known as its water vapor capacity. The amount of water vapor the air can hold depends on its temperature; warm air can hold more water vapor than cold air. When the air reaches its maximum water vapor capacity, it becomes saturated, and any additional water vapor condenses into liquid form. The temperature at which the air becomes saturated is called the dew point. At this temperature, the air is holding as much moisture as it can, and any additional cooling will cause the excess moisture to condense out of the air, forming dew or frost on surfaces. For example, on a cool morning, the temperature of the grass may be lower than the air temperature. As the air near the grass cools, it may reach its dew point, and the excess moisture in the air will condense onto the grass, forming dew. Therefore, the correct option is the dew point, which is the temperature at which the water vapor present in the air is just sufficient to saturate it.

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The given gas is at a pressure of 80 Nm^-2 and a temperature of 47^oC. To find the new pressure at a temperature of 27^oC with constant volume, we can use the ideal gas law: P₁/T₁ = P₂/T₂ where P₁ is the initial pressure, T₁ is the initial temperature, P₂ is the final pressure, and T₂ is the final temperature. Substituting the given values into the equation, we have: 80 Nm^-2 / (47 + 273) K = P₂ / (27 + 273) K Simplifying the equation, we get: P₂ = 80 Nm^-2 × (27 + 273) K / (47 + 273) K P₂ = 75 Nm^-2 Therefore, the new pressure at a temperature of 27^oC with constant volume is 75 Nm^-2.

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The best explanation for why a person suffers more severe burns when exposed to steam than boiling water is that steam possesses greater heat energy per unit-mass than boiling water. This means that when steam comes into contact with the skin, it transfers more heat energy to the skin than boiling water would at the same temperature. Additionally, steam can also spread and penetrate more easily over a wider area of the skin, causing more extensive and severe burns.

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The concave meniscus of water in a glass tube is caused by the difference in the attractive forces between the water molecules and the glass. The glass attracts the water molecules, which creates an adhesive force, but the water molecules also attract each other, creating a cohesive force. In the case of a concave meniscus, the adhesive force between the water and the glass is greater than the cohesive force between the water molecules. This causes the water at the edges of the meniscus to be pulled up towards the glass, creating a concave shape. Therefore, the answer is: - The adhesion between water and glass is greater than the cohesion between water molecules.

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The statement that is not correct about a loaded spiral spring is: "Up to the yield limit, extension is no longer proportional to the applied load." The yield limit is the point at which the material of the spring starts to deform plastically, which means that it undergoes permanent deformation even after the load is removed. Beyond the yield limit, the spring will no longer return to its original shape or form. Before the yield limit is reached, the extension of the spring is proportional to the load applied, as stated in the first option. This means that if you double the load applied to the spring, the extension will also double, as long as the elastic limit is not exceeded. Similarly, when the load is removed, the contraction of the spring is proportional to the load removed, as stated in the second option. However, once the yield limit is exceeded, the extension of the spring is no longer proportional to the applied load, as stated in the third and fourth options. This is because the spring has undergone permanent deformation, and will not return to its original shape or form. The amount of extension will depend on the load applied and the amount of plastic deformation that has occurred. The last option is a general statement about elasticity, and is not specific to loaded spiral springs. If a material regains its shape or form after deformation, it is said to be elastic. Therefore, the correct answer is option (C): "Up to the yield limit, extension is no longer proportional to the applied load."

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The reason why a concrete floor feels colder to the bare feet than a mat on the same floor during the rainy season is that the concrete floor is a better conductor of heat than the mat. Heat is transferred from a warmer object to a cooler object by three modes of heat transfer: conduction, convection, and radiation. Conduction is the transfer of heat through a material without any perceptible motion of the material. When two objects are in contact with each other, heat is transferred from the warmer object to the cooler object by conduction. In this case, when the bare feet touch the mat or the concrete floor, heat flows from the feet to the mat or the floor by conduction. The rate of heat transfer depends on the thermal conductivity of the materials. Thermal conductivity is the property of a material that determines how well it conducts heat. Concrete is a dense material and has a higher thermal conductivity than most materials used to make mats, such as rubber or fabric. This means that the concrete floor can extract heat from the bare feet more efficiently than the mat. As a result, the bare feet feel colder when in contact with the concrete floor than when in contact with the mat. Therefore, the correct option is that the concrete floor is a better conductor of heat than the mat, which results in the bare feet feeling colder when in contact with the floor than when in contact with the mat during the rainy season.

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The total momentum before the collision is equal to the total momentum after the collision (assuming no external forces act on the system). Before the collision, the first ball has a momentum of: p₁ = m₁v₁ = (0.5 kg)(10 m/s) = 5 kg m/s The second ball is at rest, so it has zero momentum: p₂ = m₂v₂ = (0.5 kg)(0 m/s) = 0 kg m/s The total momentum before the collision is: p₁ + p₂ = 5 kg m/s + 0 kg m/s = 5 kg m/s After the collision, the two balls move off together with a common velocity v. The total mass of the system is: m₁ + m₂ = 0.5 kg + 0.5 kg = 1 kg So the total momentum after the collision is: p_f = (m₁ + m₂)v_f = (1 kg)(v_f) Since the total momentum before the collision is equal to the total momentum after the collision, we have: p₁ + p₂ = p_f 5 kg m/s + 0 kg m/s = (1 kg)(v_f) v_f = 5 m/s Therefore, the common velocity of the two balls after the collision is 5 m/s. Answer: 5.0ms^-1

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The lamp has a power rating of 60W and is connected to a 220V source. We can calculate the current consumed by the lamp using Ohm's Law: I = P/V Where I is the current, P is the power and V is the voltage. So, I = 60W / 220V = 0.27A The energy consumed by the lamp in one hour can be calculated using the formula: Energy = Power x Time Where Time is the duration for which the lamp is switched on. Therefore, Energy = 60W x 1 hour = 60 Wh = 60 x 3600J = 216000J Therefore, the energy consumed by the lamp when connected to a 220V source for 1 hour is 216000J. Hence, the correct option is (a) 216000J.

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The statement "have no intermolecular attractive force" is not correct. In the gaseous state, the molecules of a substance are in constant motion, and they have different speeds. The temperature of the gas is an average measure of the kinetic energy of the molecules. However, the molecules in a gas do have intermolecular attractive forces, but these forces are much weaker than in liquids or solids. The pressure of a gas is determined by the number of molecules present and their kinetic energy.

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The terminal p.d of a battery is the voltage difference between its positive and negative terminals when it is connected to a circuit. In this case, we have a battery of emf 24V and internal resistance 4Ω connected to a resistor of 32Ω. When a current flows through the circuit, there will be a voltage drop across the internal resistance of the battery, which will reduce the voltage available at the terminals. To calculate the terminal p.d of the battery, we can use Ohm's law, which states that V = IR, where V is the voltage, I is the current, and R is the resistance. First, we need to calculate the current in the circuit using the total resistance, which is the sum of the internal resistance and the external resistance: Rtotal = Rinternal + Rexternal = 4Ω + 32Ω = 36Ω Using Ohm's law, we can calculate the current in the circuit: I = V/Rtotal I = 24V/36Ω I = 0.67A Now we can calculate the voltage drop across the internal resistance using Ohm's law: Vinternal = IRinternal Vinternal = 0.67A x 4Ω Vinternal = 2.68V Finally, we can calculate the terminal p.d of the battery by subtracting the voltage drop across the internal resistance from the emf of the battery: Vterminal = emf - Vinternal Vterminal = 24V - 2.68V Vterminal = 21.32V (approx.) Therefore, the terminal p.d of the battery is approximately 21.3V, which is the correct option.

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The correct option is III only. When an object is placed in front of a plane mirror, the image formed is virtual, upright, and laterally inverted. The virtual image means that the light rays don't actually converge at the position of the image. Instead, they appear to diverge from the image as if they are coming from behind the mirror. The magnification produced by a plane mirror is always 1, which means the size of the image is equal to the size of the object. The image distance is equal to the object distance, which means the distance between the mirror and the object is the same as the distance between the mirror and the image. Finally, the image formed by a plane mirror is laterally inverted, which means that the left and right sides of the object appear reversed in the image. Therefore, option III is incorrect because the image formed by a plane mirror is virtual, not real.

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The ability of the eye to focus objects at different distances is called "accommodation". It is the process by which the eye changes its focus to maintain a clear image of objects that are at different distances. When you look at something close up, your eye muscles contract to increase the curvature of the lens, allowing you to focus on the object. When you look at something far away, your eye muscles relax, flattening the lens to focus on the distant object. Accommodation is an important function of the eye that allows us to see objects clearly at varying distances.

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The option that cannot be used to measure the temperature of a substance is "change in color with temperature". While some substances may change color as a result of changes in temperature, this is not a reliable or precise method for measuring temperature. The color change may be subtle or difficult to distinguish, and different observers may perceive the color change differently. Additionally, the color change may be affected by other factors, such as exposure to light or chemical reactions, which can make it difficult to isolate the effect of temperature. In contrast, the other options listed are all commonly used to measure temperature. The variation of pressure with temperature can be used in devices such as gas thermometers, while the expansivity of a liquid can be used in devices such as liquid-in-glass thermometers. The change in resistance of a conductor is the principle behind resistance thermometers, while the thermoelectric effect is the principle behind thermocouples. All of these methods can provide accurate and precise measurements of temperature under the appropriate conditions.

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The total time spent by the ball in the air can be calculated using the kinematic equation: h = ut + 0.5gt^2 where h is the maximum height reached by the ball, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken for the ball to reach the maximum height and fall back to the ground. When the ball reaches its maximum height, its vertical velocity becomes zero. We can use this fact to find the maximum height reached by the ball: v = u + gt 0 = 50 - 10t t = 5 seconds u = 50 m/s h = ut + 0.5gt^2 h = (50 m/s)(5 s) + 0.5(10 m/s^2)(5 s)^2 h = 125 meters The time taken for the ball to reach the maximum height and fall back to the ground is twice the time taken for the ball to reach the maximum height: total time = 2t = 2 x 5s = 10s Therefore, the total time spent by the ball in the air is 10 seconds. Hence, the correct option is (C) 10.0s.

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The slope of a straight line displacement-time graph indicates the velocity of an object. Velocity is the rate at which an object changes its position with respect to time. It is a vector quantity, which means that it has both magnitude (speed) and direction. The slope of a displacement-time graph represents the rate of change of displacement with respect to time, which is the definition of velocity. If the slope of the displacement-time graph is constant, then the velocity is uniform. This means that the object is moving at a constant speed in a straight line. If the slope is positive, then the velocity is positive, which means that the object is moving in the positive direction. If the slope is negative, then the velocity is negative, which means that the object is moving in the negative direction. If the slope of the displacement-time graph is changing, then the velocity is not uniform. This means that the object is either accelerating or decelerating. If the slope is becoming steeper, then the object is accelerating. If the slope is becoming less steep, then the object is decelerating. Therefore, the correct option for the slope of a straight line displacement-time graph is uniform velocity, which is the rate of change of displacement with respect to time.

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(a) Labelled diagram of a vacuum flask

A vacuum flask minimizes heat exchange as follows:

• The vacuum between the double glass walls prevents heat transfer by conduction and convection.
• The silvered surfaces reflect thermal radiation, thereby reducing heat transfer by radiation.
• The cork or plastic stopper is a poor conductor of heat, while the narrow neck reduces convection and evaporation through the top.

(b) Boyle's law

Boyle's law states that the volume of a fixed mass of gas is inversely proportional to its pressure, provided that its temperature remains constant.

Thus,

\[PV=\text{constant}\qquad\text{or}\qquad P_1V_1=P_2V_2.\]

Since the capillary tube has a uniform cross-sectional area, the volume of the trapped air is proportional to its length. Therefore,

\[P_1L_1=P_2L_2.\]

Initially, with the open end uppermost, the pressure of the trapped air is:

\[P_1=76+15=91\ \text{cm Hg},\qquad L_1=20\ \text{cm}.\]

(i) Tube held horizontally

There is no vertical mercury head acting on the trapped air, so:

\[P_2=76\ \text{cm Hg}.\]

\[91\times20=76\times L_2\]

\[L_2=\frac{1820}{76}=23.95\ \text{cm}\approx24\ \text{cm}.\]

Length of air column = \(24\ \text{cm}\).

(ii) Tube held vertically with the open end underneath

The mercury thread now reduces the pressure on the trapped air:

\[P_2=76-15=61\ \text{cm Hg}.\]

\[91\times20=61\times L_2\]

\[L_2=\frac{1820}{61}=29.84\ \text{cm}\approx30\ \text{cm}.\]

Length of air column = \(30\ \text{cm}\).

(c) A clinical thermometer has a limited range, usually about \(35^\circ\text{C}\) to \(42^\circ\text{C}\). In boiling water at \(100^\circ\text{C}\), the mercury expands excessively and may force its way into the upper end of the capillary tube, cracking or damaging the thermometer. It should therefore not be sterilized in boiling water.

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(a)(i) Electric field intensity, E, at a point is the force experienced per unit positive test charge placed at that point.

\[E=\frac{F}{q}\]

It is a vector quantity. Its SI unit is \(\mathrm{N\,C^{-1}}\) (or \(\mathrm{V\,m^{-1}}\)), and its direction is the direction of the force on a positive test charge.

(ii) Electric lines of force are imaginary lines used to show an electric field. The tangent to a field line at any point gives the direction of the field. They emerge from positive charges and terminate on negative charges; closer spacing indicates a stronger field, and field lines never intersect.

(b) Point \(P\) lies between the charges, \(0.050\,\mathrm{m}\) from \(-q\) and \(0.030\,\mathrm{m}\) from \(+q\). Taking \(k=\dfrac{1}{4\pi\varepsilon_0}=9.0\times10^9\,\mathrm{N\,m^2\,C^{-2}}\):

Field at \(P\) due to \(-q\):

\[E_{-}=\frac{kq}{(0.050)^2}=\frac{(9.0\times10^9)(5.0\times10^{-8})}{(0.050)^2}=1.80\times10^5\,\mathrm{N\,C^{-1}}\]

Field at \(P\) due to \(+q\):

\[E_{+}=\frac{kq}{(0.030)^2}=\frac{(9.0\times10^9)(5.0\times10^{-8})}{(0.030)^2}=5.00\times10^5\,\mathrm{N\,C^{-1}}\]

At \(P\), both fields are directed from \(+q\) towards \(-q\). Therefore,

\[E=E_{+}+E_{-}=5.00\times10^5+1.80\times10^5=6.80\times10^5\,\mathrm{N\,C^{-1}}\]

Resultant field intensity at \(P\) = \(6.8\times10^5\,\mathrm{N\,C^{-1}}\), directed towards the negative charge (from \(+q\) to \(-q\)).

The electric lines of force for the two unlike point charges are shown below.

(c)

Given: \(f=25\,\mathrm{Hz}\), \(C=10\,\mu\mathrm{F}=10\times10^{-6}\,\mathrm{F}\), \(R=1000\,\Omega\), and \(V=90\,\mathrm{V_{rms}}\).

(i) Capacitive reactance

\[X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi(25)(10\times10^{-6})}=636.6\,\Omega\]

(ii) Impedance

\[Z=\sqrt{R^2+X_C^2}=\sqrt{1000^2+636.6^2}=1185.4\,\Omega\]

(iii) Current through the circuit

\[I=\frac{V}{Z}=\frac{90}{1185.4}=7.59\times10^{-2}\,\mathrm{A}=0.0759\,\mathrm{A_{rms}}\]

(iv) Voltage across the capacitor

\[V_C=IX_C=(0.0759)(636.6)=48.3\,\mathrm{V_{rms}}\]

(v) Average power used in the circuit

Only the resistor dissipates average power:

\[P=I^2R=(0.0759)^2(1000)=5.76\,\mathrm{W}\]

Antwortdetails

(a) Uses of a converging lens

(i) Igniting carbon paper: Hold the carbon paper at the principal focus, F, of the converging lens and direct the lens towards the Sun. The parallel rays from the Sun are brought to a very small bright spot at F. The heat energy is concentrated there and ignites the carbon paper.

(ii) Producing an enlarged picture on a screen: Place the object or slide between F and 2F of the converging lens. A real, inverted and magnified image is formed beyond 2F; a screen is placed at this image position.

(iii) Correcting an eye defect: A converging lens is used to correct long-sightedness (hypermetropia). In a long-sighted eye, rays from a near object would be focused behind the retina. The spectacle lens converges the rays before they enter the eye, so that the eye lens forms the image on the retina.

(b) Mechanical wave: A mechanical wave is a disturbance that requires a material medium, such as a solid, liquid or gas, for its propagation. It cannot travel through a vacuum. Examples are sound waves and water waves.

Experiment showing that sound needs a material medium: An electric bell is placed inside an airtight bell jar connected to a vacuum pump. When the switch is closed, the bell rings and its hammer is seen striking the gong. While air is present in the jar, the sound is heard clearly. As the pump removes the air, the sound becomes fainter. When the jar is nearly evacuated, the hammer is still seen striking the gong but little or no sound is heard. Therefore, sound requires a material medium, in this case air, for transmission.

Characteristics of sound

1. Loudness (intensity): depends on the amplitude of vibration.
2. Pitch: depends on the frequency of vibration.
3. Quality (timbre): depends on the number and relative strengths of the overtones or harmonics present.

Antwortdetails

(a) Moment of a force about a point

The moment of a force about a point is the turning effect of the force about that point. It is equal to the product of the force and the perpendicular distance of its line of action from the point.

\[\text{Moment}=F\times d\]

where \(F\) is the force and \(d\) is the perpendicular distance from the pivot to the line of action of the force. The SI unit is newton metre, \(\text{N m}\).

(b) Conditions for equilibrium of coplanar parallel forces

1. The algebraic sum of the forces must be zero, that is, total upward force equals total downward force.
2. The algebraic sum of moments about any point must be zero, that is, total clockwise moment equals total anticlockwise moment.

The metre rule balances at the 48 cm mark, so its weight acts at the 48 cm mark.

(i) Mass of the metre rule

Taking moments about the balance point at 30 cm:

\[60(30-6)=M(48-30)\]

\[60\times24=M\times18\]

\[M=\frac{60\times24}{18}=80\text{ g}\]

Therefore, the mass of the metre rule is 80 g.

(ii) New balance point

Let the new balance point be \(x\) cm from the zero end. The 60 g body is at 13 cm and the rule's weight acts at 48 cm.

Taking moments about the new balance point:

\[60(x-13)=80(48-x)\]

\[60x-780=3840-80x\]

\[140x=4620\]

\[x=33\text{ cm}\]

Therefore, the balance point is 33 cm from the zero end.

(c) Relation between efficiency, mechanical advantage and velocity ratio

\[E=\frac{\text{work output}}{\text{work input}}\times100\%\]

\[E=\frac{\text{Load}\times\text{distance moved by load}}{\text{Effort}\times\text{distance moved by effort}}\times100\%\]

\[E=\left(\frac{\text{Load}}{\text{Effort}}\right)\left(\frac{\text{distance moved by load}}{\text{distance moved by effort}}\right)\times100\%\]

Since \(\text{M.A.}=\frac{\text{Load}}{\text{Effort}}\) and \(\text{V.R.}=\frac{\text{distance moved by effort}}{\text{distance moved by load}}\),

\[\boxed{E=\frac{\text{M.A.}}{\text{V.R.}}\times100\%}\]

Work done by the person

Work output in raising the load is:

\[W_{\text{out}}=mgh=200\times10\times3.0=6000\text{ J}\]

\[80\%=\frac{W_{\text{out}}}{W_{\text{in}}}\times100\%\]

\[0.80=\frac{6000}{W_{\text{in}}}\]

\[W_{\text{in}}=\frac{6000}{0.80}=7500\text{ J}\]

Therefore, the work done by the person is \(7.5\times10^3\text{ J}\).