WAEC SSCE - Physics - 1991

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When the key is open, the two capacitors are not connected and the charge on each of them is zero. The energy stored in capacitor C1 is given by the formula: W = (1/2) * C1 * V^2, where V is the voltage across capacitor C1. When the key is closed, the two capacitors are connected in parallel, and a charge Q will flow from one plate of C1 to the other plate of C2 until the voltage across both capacitors is the same. Let the voltage across both capacitors be V. Then, the charge on C1 will be Q/2, and the charge on C2 will be Q. The total energy stored in the system can be calculated as follows: W(total) = (1/2) * C1 * V^2 + (1/2) * C2 * V^2 Substituting C2 = 2C1 and Q = CV, we get: W(total) = (1/2) * C1 * V^2 + (1/2) * 2C1 * V^2 = (1/2) * 3C1 * V^2 = (3/2) * W Therefore, the total energy stored in the system when the key is closed and the system is allowed to attain electrical equilibrium is (3/2) times the energy stored in C1 when the key is open. Hence, the correct option is 3W.

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The part of the camera that corresponds to the iris of the eye is the diaphragm. Just like the iris controls the amount of light entering the eye, the diaphragm controls the amount of light entering the camera. It is a circular opening in the camera lens that can be adjusted to vary the size of the aperture. When the diaphragm is wider, more light enters the camera, and when it is narrower, less light enters. This helps control the depth of field and the amount of light that hits the camera's sensor or film.

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To calculate the number of turns in the secondary coil of the transformer, we need to use the formula: Np/Ns = Vp/Vs Where Np is the number of turns in the primary coil, Ns is the number of turns in the secondary coil, Vp is the voltage in the primary coil, and Vs is the voltage in the secondary coil. In this case, we know that the voltage in the primary coil is 240V and the voltage in the secondary coil is 8V. We also know that the number of turns in the primary coil is 900. Plugging these values into the formula, we get: 900/Ns = 240/8 Simplifying this equation, we get: 900/Ns = 30 To solve for Ns, we can multiply both sides by Ns: 900 = 30Ns Dividing both sides by 30, we get: Ns = 30 Therefore, the number of turns in the secondary coil of the transformer is 30. So, the correct option is "30".

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The unit of pressure is force per unit area, while the unit of volume is length cubed. Therefore, the product of pressure and volume is given by force times length cubed, which is equivalent to work, the amount of energy transferred when a force of one newton is applied over a distance of one meter. Therefore, the product PV has the same unit as work, which is joule (J).

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The incorrect statement about waves is iii. A wavefront is not a circle which is common to particles that are in the same state of disturbance. Rather, a wavefront is an imaginary surface that connects all points in space that are reached by a wave at the same time during its propagation. Hence, the correct answer is (e) ii and iii only. (i) A wavefront is a line that connects all particles in the medium that are vibrating in phase, meaning that their displacement from equilibrium is the same at any given moment in time. This means that they reach their maximum and minimum amplitudes at the same time. (ii) The direction of propagation of a wave is always perpendicular to the wavefront. This is because each point on the wavefront is at the same phase of vibration and so has the same displacement from equilibrium at any given moment in time. Therefore, the wavefront itself is a surface of constant phase, and the direction of propagation is the normal to this surface. (iii) As mentioned earlier, a wavefront is not a circle which is common to particles that are in the same state of disturbance. However, it can be a circle in the case of a spherical wave, which emanates from a point source and spreads out uniformly in all directions.

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Melting ice cools an orange drink better than the same mass of ice-cold water because ice absorbs latent heat during melting. Latent heat is the heat energy required to change the state of a substance without changing its temperature. When ice melts, it absorbs latent heat from the drink to overcome the intermolecular forces holding its particles together. This absorption of latent heat results in cooling of the drink. On the other hand, ice-cold water has already reached its melting point, and there is no further absorption of latent heat during cooling. Water has a higher specific heat than ice, which means it can absorb more heat energy without changing its temperature. However, this does not contribute to better cooling of the drink. Option (i) is incorrect because ice-cold water is actually at a lower temperature than melting ice. Option (iii) is also incorrect because while ice floats, it does not cool the air above the drink significantly. Option (v) is not entirely correct because while ice can make better thermal contact than water, it is the absorption of latent heat that makes it more effective in cooling the drink. Therefore, the correct answer is option (iv) ice absorbs latent heat during melting.

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The unit of stress is Nm^-2 (Newtons per square meter), also known as Pascal (Pa). Stress is defined as force per unit area and is a measure of the internal forces acting on a material. When a force is applied to a material, it creates internal forces that tend to resist the deformation or change in shape. Stress is the measure of these internal forces per unit area. The unit Nm represents work or energy, while N represents force, and Nm² does not have a physical meaning.

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The velocity of sound in air can be calculated using the formula: velocity = distance / time In this case, the distance travelled by the sound is twice the distance from the man to the wall, since the sound has to travel to the wall and back. So, the distance travelled by the sound is: 2 x 300m = 600m The time taken for the sound to travel this distance (to the wall and back) is: 1.8s So, using the formula: velocity = distance / time velocity = 600m / 1.8s velocity = 333.3ms^-1 Therefore, the velocity of sound in air is 333.3ms^-1. Hence, the correct option is ii. 333.3ms^-1.

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To calculate the specific latent heat of the solid, we need to use the formula: Q = mL where Q is the amount of energy supplied by the immersion heater, m is the mass of the solid, and L is the specific latent heat of the solid. First, we need to calculate the amount of energy supplied by the immersion heater. We know that the heater has a power output of 90W and it is used for 5 minutes, so the total energy supplied is: Q = Pt = 90W x 5min x 60s/min = 27,000 J Next, we can use this value of Q and the mass of the solid, which is 160g, to calculate the specific latent heat L: L = Q/m = 27,000 J / 160g = 168.75 Jg^-1 Therefore, the specific latent heat of the solid is 168.75 Jg^-1. Option (D) 168.75 Jg^-1 is the correct answer.

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To solve this problem, we can use the formula: h = (ρm/ρa) * (P0 - P) where: h = height of the plane above the ground ρm = density of mercury (13.6 g/cm^3) ρa = density of air (0.00136 g/cm^3) P0 = atmospheric pressure at ground level (75 cm of Hg) P = atmospheric pressure at the height of the plane (63 cm of Hg) First, we need to convert the units of the densities from g/cm^3 to kg/m^3 to be consistent with the units of the atmospheric pressure in meters of mercury (m of Hg): ρm = 13.6 * 1000 kg/m^3 = 13600 kg/m^3 ρa = 0.00136 * 1000 kg/m^3 = 1.36 kg/m^3 Now, we can plug in the values and solve for h: h = (13600/1.36) * (75 - 63) h = 10000 * 12 h = 120000 meters Therefore, the height of the plane above the ground is 120,000 meters. Note: This answer seems unreasonable as it is much higher than the typical cruising altitude of commercial airplanes. This may be due to a mistake in the given information or in the calculations.

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In the apparatus used to determine the specific latent heat of vaporisation of steam, the steam trap is used to ensure that only dry steam gets into the calorimeter. The steam trap works by allowing the steam to pass through it, but trapping any condensed steam or water droplets that may be present in the steam. This is important because if any water droplets or condensed steam get into the calorimeter, they will add to the heat energy in the system and affect the accuracy of the measurement. By trapping any condensed steam, the steam trap ensures that only dry steam gets into the calorimeter, which allows for a more accurate measurement of the specific latent heat of vaporisation of steam. Therefore, the correct option is: ensures that only dry steam gets into the calorimeter.

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We can solve this problem using the kinematic equations of motion. Since the ball is projected horizontally, its initial vertical velocity is zero. We can use the following equation to find the height of the hill: h = (1/2)gt^2 Where h is the height of the hill, g is the acceleration due to gravity, and t is the time taken for the ball to reach the ground. In this case, g = 10ms^-2 and t = 4s. Plugging these values into the equation, we get: h = (1/2)(10)(4)^2 = 80m Therefore, the height of the hill is 80 meters. This is option (C). To summarize, the ball is projected horizontally with a velocity of 20m/s, which means its initial vertical velocity is zero. Using the kinematic equation for displacement, we can find the height of the hill. The ball takes 4 seconds to reach the ground, so we substitute this value along with the acceleration due to gravity into the equation. The resulting answer is 80 meters, which is the height of the hill.

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The observation that the sound from a bell in an enclosed jar gradually faints away while the jar is being evacuated can be explained by the fact that there is no more material medium for the sound waves to propagate through. Sound waves are vibrations that propagate through a medium such as air, water, or solids. When the jar is evacuated, the air is pumped out, resulting in a decrease in pressure inside the jar. As the pressure decreases, the density of the air inside the jar decreases as well. Sound waves require a medium to travel through, and in this case, there is less and less air inside the jar, resulting in fewer particles available to transmit the sound waves. Eventually, when the jar is fully evacuated, there is no more air left inside the jar to transmit the sound waves. Therefore, the correct option is: there is no more material medium.

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Since the body is moving with uniform acceleration, the graph of its velocity vs time will be a straight line. Let the initial velocity of the body be u, and the acceleration be a. From the two given points, we can determine two equations: 1. At t = 5 s, v = 15 m/s: 15 = u + 5a 2. At t = 20 s, v = 60 m/s: 60 = u + 20a Subtracting equation 1 from equation 2, we get: 45 = 15a a = 3 m/s^2 Therefore, the acceleration of the body is 3.00 ms^-2. is the correct answer.

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To calculate the time it takes for the orange fruit to hit the ground, we can use the following formula: d = 1/2 * g * t^2 where d is the distance (in meters) the orange falls, g is the acceleration due to gravity (in meters per second squared), and t is the time (in seconds) it takes for the orange to fall. In this case, the orange falls from a height of 45m, and g is 10m/s^2. We can plug these values into the formula and solve for t: 45 = 1/2 * 10 * t^2 Simplifying the equation: t^2 = 9 t = 3 Therefore, it takes 3 seconds for the orange fruit to hit the ground. This is the answer to the problem.

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A stationary wave is a type of wave that appears to be standing still, even though it is made up of two waves traveling in opposite directions. Option i describes a resonance tube closed at one end and a vibrating tuning fork held near the end. In this situation, the sound wave produced by the tuning fork travels down the resonance tube and reflects off the closed end, creating a stationary wave. Option ii describes a string that is tightly stretched between two points and plucked at its middle. In this situation, the string vibrates back and forth, creating a wave that travels along the string and reflects back when it reaches the ends, creating a stationary wave. Option iii describes a tuning fork vibrating in air, which produces a sound wave that travels through the air as a longitudinal wave. This wave does not create a stationary wave since it does not reflect back and interfere with itself. Therefore, the correct answer is option i and ii only.

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The saturation vapor pressure of a liquid depends on its temperature. When a liquid evaporates, it turns into a gas or vapor. This process of evaporation depends on the energy of the liquid molecules. The higher the temperature, the more energy the molecules have, and the more likely they are to escape from the surface of the liquid and become a gas. As the concentration of vapor molecules increases above a liquid surface, some of them may condense back into the liquid phase, and this creates an equilibrium between the liquid and vapor phases, called saturation. The saturation vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid phase at a given temperature. So, as the temperature of the liquid increases, the saturation vapor pressure increases, meaning more molecules are in the gas phase. On the other hand, as the temperature decreases, the saturation vapor pressure decreases, indicating fewer molecules in the gas phase. Therefore, the saturation vapor pressure of a liquid is determined by its temperature and is independent of the volume, mass, density, or pressure of the liquid.

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The kinetic energy of the ejected electrons can be calculated using the equation: Kinetic energy of electron = Energy of incident radiation - Work function of the metal Substituting the given values, we have: Kinetic energy of electron = 6.86ev - 4.65ev Kinetic energy of electron = 2.21ev Therefore, the kinetic energy of the electrons ejected from the surface of the metal is 2.21ev. Hence, the correct option is (b) 2.21ev.

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We can use the combined gas law to solve this problem. The combined gas law states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas, assuming constant mass. Mathematically, this can be written as: P₁V₁/T₁ = P₂V₂/T₂ where P is pressure, V is volume, T is temperature, and the subscripts 1 and 2 refer to the initial and final states, respectively. We are told that the initial volume V₁ is 600 cm³ and the initial temperature T₁ is 27^oC = 300K. We also know that the pressure P remains constant throughout the process, and that the final temperature T₂ is 0^oC = 273K. We can solve for the final volume V₂: P₁V₁/T₁ = P₂V₂/T₂ V₂ = (P₁/P₂) * (T₂/T₁) * V₁ Since the pressure is constant, we can cancel it out, and substitute in the given values: V₂ = (273K/300K) * 600 cm³ = 546 cm³ Therefore, the change in volume is 600 cm³ - 546 cm³ = 54 cm³. So, the correct answer is 54 cm³.

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In physics, a fundamental quantity is a physical quantity that cannot be defined in terms of other physical quantities. These quantities are also known as base quantities or fundamental units. The seven fundamental quantities in the International System of Units (SI) are length, mass, time, electric current, temperature, amount of substance, and luminous intensity. Out of the options given, "length" is a fundamental quantity because it is one of the seven base quantities in the SI system. It is defined as the distance between two points in space, and it is measured in units such as meters, feet, or miles. The other options, such as "speed," "density," "impulse," and "energy," are all derived quantities, which means that they can be expressed in terms of one or more of the fundamental quantities. For example, speed is defined as the rate at which an object changes its position with respect to time, and it is derived from the fundamental quantities of length and time. Therefore, the correct option is "length," as it is a fundamental quantity.

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A particle of charge q and mass m moving with a velocity v enters a uniform magnetic field B in the direction of the field. The force on the particle is given by the equation F = qVB sinθ, where θ is the angle between the velocity vector and the magnetic field vector. In this case, since the particle enters the field in the direction of the field, θ = 0, and sinθ = 0. Therefore, the force on the particle is zero (F = qVB sinθ = qVB(0) = 0). Option (d) is correct - the force on the particle is zero. Option (a) is incorrect because it represents the formula for the magnitude of the force on a charged particle moving perpendicular to the magnetic field. Option (b) is incorrect because it represents the formula for the acceleration of a charged particle in a magnetic field. Option (c) is incorrect because it represents the formula for the radius of the circular path followed by a charged particle moving perpendicular to the magnetic field. Therefore, the correct answer is - O.

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Radio waves are not mechanical waves. Mechanical waves are waves that require a physical medium, such as a solid, liquid, or gas, to travel through. They transfer energy through the vibration of particles in the medium. On the other hand, radio waves are a type of electromagnetic wave, which means they do not require a physical medium to travel through. They can travel through a vacuum, such as space, and are created by the acceleration of electric charges. Radio waves are used for communication, including radio and television broadcasting, as well as cellular and satellite communication. Therefore, the answer is option (iii) radio waves.

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A body that moves with a constant speed but has an acceleration is moving in a circular path. Acceleration is the rate at which the velocity of an object changes. When an object moves in a circular path, it is constantly changing direction, even if it is moving at a constant speed. This means that its velocity is changing, and therefore, it has an acceleration. The direction of the acceleration is always towards the center of the circular path, and its magnitude is given by the formula a = v^2/r, where a is the acceleration, v is the speed of the object, and r is the radius of the circular path. Therefore, the correct option is: moves in a circle.

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The skin of a talking drum performs a vibratory motion when it is being struck with the drum stick. When the drum is struck, the skin vibrates back and forth, producing sound waves that travel through the air. The skin moves in a series of up-and-down motions that are perpendicular to the surface of the drum. The shape of the drum, and the tension of the skin, determine the frequency of the vibration and the pitch of the resulting sound. The player can vary the pitch by squeezing the drum under their arm or by applying pressure to the skin with their non-dominant hand. Therefore, the correct option is vibratory.

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Linear expansivity is a measure of how much a material changes in length when its temperature changes. It is denoted by the Greek letter alpha (α) and is expressed in units of K^-1. The formula for linear expansivity is: α = ΔL / (L_i * ΔT) Where: ΔL = change in length L_i = initial length ΔT = change in temperature Using the values given in the question, we have: ΔL = 0.020 m L_i = 20 m ΔT = (55 - 5) = 50 K Substituting these values into the formula, we get: α = 0.020 / (20 * 50) = 2.0 x 10^-5 K^-1 Therefore, the linear expansivity of the wire is 2.0 x 10^-5 K^-1. Answer choice (C) is the correct answer.

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The kinetic energy of the photoelectrons ejected from a metal surface when irradiated depends on the frequency of the radiation. This is known as the photoelectric effect. When a photon of light is absorbed by a metal surface, it can transfer its energy to an electron within the metal, causing the electron to be ejected from the surface. The amount of energy transferred to the electron depends on the frequency of the photon, which is related to its wavelength. Photons with higher frequencies (shorter wavelengths) have more energy than photons with lower frequencies (longer wavelengths), and thus can transfer more energy to the ejected electron, resulting in a higher kinetic energy. Therefore, the frequency of the radiation is the key factor that determines the kinetic energy of the ejected electrons.

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From the two diagrams, we can see that the heights of the mercury columns in both the open and closed ends of the capillary tube are different. This difference in height is due to the atmospheric pressure acting on the surface of the mercury in the dish. Let h₁ and h₂ be the heights of the mercury columns in the two arrangements, and let d be the density of mercury. For the first arrangement, we have: h₁ = 7 cm h₂ = 6 cm The pressure difference between the two ends of the capillary tube is given by the difference in height of the mercury columns: ΔP = dgh where g is the acceleration due to gravity. ΔP = (13.6 x 10³ kg/m³) x (10.0 m/s²) x (0.01 m) x (h₁ - h₂) ΔP = 1.36 x 10³ (h₁ - h₂) Pa For the second arrangement, we have: h₁ = 75 cm h₂ = 74 cm Using the same formula, we get: ΔP = 1.36 x 10³ (h₁ - h₂) Pa ΔP = 1.36 x 10³ (75 - 74) Pa ΔP = 1.36 x 10³ Pa To find the pressure of the atmosphere, we need to add this pressure difference to the atmospheric pressure: P_atm = P₀ + ΔP where P₀ is the atmospheric pressure at the surface of the mercury in the dish. Since the height of the mercury column in the dish is 76 cm, we have: P₀ = dgh P₀ = (13.6 x 10³ kg/m³) x (10.0 m/s²) x (0.01 m) x (76 cm) P₀ = 1.032 x 10⁵ Pa Therefore, the atmospheric pressure is: P_atm = P₀ + ΔP P_atm = 1.032 x 10⁵ Pa + 1.36 x 10³ Pa P_atm = 1.046 x 10⁵ Pa Converting this to cm of Hg, we get: P_atm = 1.046 x 10⁵ Pa x (1 cm/133.322 Pa) P_atm = 784.8 cm of Hg Therefore, the pressure of the atmosphere is approximately 784.8 cm of Hg. The answer is closest to 75 cm

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The work done in accelerating the electron is given by W = qV where q is the charge of the electron and V is the potential difference. The potential difference is given as 40 kV, which is equivalent to 40 x 10^3 V. Therefore, the work done in accelerating the electron is: W = (1.6 x 10^-19 C) x (40 x 10^3 V) = 6.4 x 10^-15 J This work done is equal to the kinetic energy gained by the electron since it started from rest. Therefore, the kinetic energy of the electron is: K.E = 6.4 x 10^-15 J Hence, the correct option is: 3.2 x 10^-15 J.

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An induction coil is generally used to produce a large output voltage. An induction coil is a type of transformer that uses a magnetic field to convert a low voltage (input voltage) to a high voltage (output voltage). The coil works on the principle of electromagnetic induction, where a changing magnetic field induces an electric current in a nearby conductor. In an induction coil, the primary coil is connected to a source of electrical energy, and the secondary coil is connected to the load. When an electric current flows through the primary coil, it creates a changing magnetic field that induces an electric current in the secondary coil, resulting in a large output voltage. The ratio of the number of turns in the primary coil to the number of turns in the secondary coil determines the voltage transformation ratio.

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(a)(i) Temperature and heat

Temperature	Heat
Temperature is the degree of hotness or coldness of a body. It determines the direction in which heat flows.	Heat is energy transferred from a body at a higher temperature to a body at a lower temperature because of a temperature difference.
It is measured in kelvin, K, the SI unit. Degree Celsius, b0C, is also commonly used.	Its SI unit is the joule, J.

(a)(ii) Two physical properties used in thermometry are:

1. change in volume of a liquid with temperature;
2. change in electrical resistance of a conductor with temperature.

(b)(i) Determination of the upper fixed point, or steam point

The apparatus is arranged as shown below.

Pure water is boiled in a hypsometer. The bulb of the mercury-in-glass thermometer is surrounded by dry steam above the boiling water. The pressure of the steam is measured with the manometer and is adjusted to standard atmospheric pressure, 76 cm Hg (760 mm Hg). When the mercury thread becomes steady, its level is marked on the stem. This mark is the upper fixed point, equal to 100 b0C.

Precaution: Ensure that the thermometer bulb is completely surrounded by steam and does not touch the boiling water or the wall of the vessel.

(b)(ii)

• Advantage: A constant-volume gas thermometer gives very accurate measurements over a wide temperature range, since the expansion of the containing glass is negligible compared with the change in pressure of the gas. It is therefore suitable as a standard thermometer for calibration.
• Reason it is seldom used routinely: It is bulky, delicate and inconvenient to handle, and it gives readings slowly.

(c) Why evaporation causes cooling

Liquid molecules are in continual random motion and have different kinetic energies. At the surface, the fastest molecules, having sufficiently high kinetic energy, escape from the liquid as vapour. These molecules carry away more than the average kinetic energy. The average kinetic energy of the molecules left in the liquid therefore decreases. Since temperature is proportional to the average kinetic energy of the molecules, the temperature of the remaining liquid falls, causing cooling.

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(a)(i) Modern X-ray (Coolidge) tube

The tube is highly evacuated. A low-voltage supply heats the tungsten filament at the cathode. The hot filament emits electrons by thermionic emission. A very high potential difference between the cathode and the anode accelerates and focuses the electrons towards the tungsten target.

When the high-speed electrons strike the tungsten target, they are suddenly decelerated. A small fraction of their kinetic energy is emitted as X-rays, which leave through the window. Most of the energy becomes heat; hence the tungsten target is mounted in copper and the anode is cooled.

(a)(ii) Energy transformation

Electrical energy is converted to kinetic energy of the electrons, and then mainly to heat energy and partly to X-ray electromagnetic radiation:

\[\text{electrical energy} \rightarrow \text{kinetic energy of electrons} \rightarrow \text{heat energy} + \text{X-ray energy}.\]

(b) Hardness and intensity of X-rays

• Hardness is the penetrating power, or quality, of an X-ray beam. Hard X-rays have high frequency, short wavelength and high photon energy, and are therefore more penetrating. Their hardness is increased by increasing the accelerating potential difference across the tube. X-rays produced at lower voltage are softer and less penetrating.
• Intensity is the quantity of X-rays emitted per second, that is, the number of X-ray photons in the beam. It is increased by increasing the filament heating current, since more electrons are then emitted and strike the target.

(c)(i) Uses of X-rays

1. Radiography of the body, for example to locate fractured bones.
2. Detecting internal cracks and defects in welds, metal castings and other engineering materials.
3. Studying crystal structure by X-ray diffraction.

(c)(ii) Hazard and precautions

Hazard: Over-exposure damages living cells and tissues and may cause radiation burns, mutations or cancer.

Safety precautions:

1. Use lead shielding, such as lead-lined screens or a lead apron, between the operator and the X-ray source.
2. Keep exposure time as short as possible and operate the equipment from a safe distance, outside the direct beam.

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(a) Reactance and impedance

Reactance is the opposition offered to alternating current by an inductor or a capacitor. It is measured in ohms, \(\Omega\).

For an inductor, \(X_L=2\pi fL\), while for a capacitor, \(X_C=\dfrac{1}{2\pi fC}\).

Impedance is the total opposition offered to alternating current by a circuit containing resistance and reactance. For a series RLC circuit,

\[Z=\sqrt{R^2+(X_L-X_C)^2}.\]

(b) Vector diagram

Take the current, and hence \(V_R\), as the horizontal reference. \(V_L\) leads the current by \(90^\circ\), while \(V_C\) lags the current by \(90^\circ\).

From the voltage phasor diagram,

\[V^2=V_R^2+(V_L-V_C)^2.\]

Given \(V=240\text{ V}\), \(V_R=140\text{ V}\), and \(V_L=50\text{ V}\),

\[240^2=140^2+(50-V_C)^2\]

\[(50-V_C)^2=57600-19600=38000\]

\[50-V_C=-\sqrt{38000}=-194.94\]

\[V_C=244.94\text{ V}.\]

(i) Potential difference across the capacitor:

\[\boxed{V_C\approx245\text{ V}}\]

(ii) Capacitance of the capacitor

\[X_C=\frac{V_C}{I}=\frac{244.94}{10}=24.49\ \Omega\]

\[C=\frac{1}{2\pi fX_C}=\frac{1}{2\pi\times50\times24.49}\]

\[\boxed{C=1.30\times10^{-4}\text{ F}=130\ \mu\text{F}}\]

(iii) Inductance of the inductor

\[X_L=\frac{V_L}{I}=\frac{50}{10}=5.0\ \Omega\]

\[L=\frac{X_L}{2\pi f}=\frac{5.0}{2\pi\times50}\]

\[\boxed{L=1.59\times10^{-2}\text{ H}\approx0.016\text{ H}}\]

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(a)

Uniform acceleration is acceleration for which the velocity changes by equal amounts in equal intervals of time. Thus, the acceleration is constant.

Average speed is the total distance travelled divided by the total time taken:

\[\text{Average speed}=\frac{\text{total distance travelled}}{\text{total time taken}}.\]

(b) The successive velocity-time coordinates are:

Time, \(t\) (s)	Velocity, \(v\) (m s\(^{-1}\))	Explanation
0	0	Body starts from rest.
30	240	\(v=0+(8.0\times30)=240\).
50	340	\(v=240+(5.0\times20)=340\).
110	340	Speed is maintained for 60 s.
130	0	Body comes to rest in 20 s.

Plot the points and join successive points with straight lines:

(c)

(i) Maximum speed

\[\boxed{340\ \text{m s}^{-1}}\]

(ii) Average retardation while the body is being brought to rest

\[a=\frac{v-u}{t}=\frac{0-340}{20}=-17\ \text{m s}^{-2}.\]

Hence, the average retardation is \(\boxed{17\ \text{m s}^{-2}}\).

(iii) Total distance travelled during the first 50 s

The distance is the area under the velocity-time graph from \(0\) to \(50\) s:

\[\begin{aligned} s&=\frac{1}{2}(30)(240)+\frac{1}{2}(240+340)(20)\\&=3600+5800\\&=\boxed{9400\ \text{m}}.\end{aligned}\]

(iv) Average speed during the interval in (ii)

During the 20 s retardation interval, the distance travelled is the triangular area:

\[s=\frac{1}{2}(20)(340)=3400\ \text{m}.\]

\[\text{Average speed}=\frac{3400}{20}=\boxed{170\ \text{m s}^{-1}}.\]