WAEC SSCE - Physics - 2012

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The formula for the inductive reactance is X_L = 2πfL, where X_L is the inductive reactance in ohms, f is the frequency in Hertz and L is the inductance in Henrys. We are given that the mains supply has a frequency of 50Hz, and that the current through the inductor is 1.5A. We also know that the voltage across the inductor is V = I X_L, where V is the voltage in volts. The voltage across the inductor is given as 24V, so we can use Ohm's law to find the inductive reactance: X_L = V / I = 24V / 1.5A = 16Ω We can now use the formula X_L = 2πfL to find the inductance: L = X_L / 2πf = 16Ω / (2π x 50Hz) = 0.051H ≈ 5.1 x 10^-2H Therefore, the inductance of the inductor is approximately 5.1 x 10^-2H. The correct option is (d).

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The device used to determine the relative density of an acid is a hydrometer. A hydrometer is an instrument used to measure the density or specific gravity of a liquid. It works based on Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. The hydrometer consists of a glass tube with a bulb at the bottom, and a scale to measure the density. When the hydrometer is placed in the acid, it floats and sinks to a certain level depending on the density of the acid. The density is then read off the scale at the level where the surface of the liquid intersects the scale on the hydrometer. Therefore, a hydrometer is used to determine the relative density of an acid.

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The magnitude of the acceleration is given by the formula: acceleration = resultant force / mass In this question, the resultant force is given as 15N and the mass is 250g which is equivalent to 0.25kg. Therefore, acceleration = 15N / 0.25kg = 60.00ms^-2 Hence, the correct option is 60.00ms^-2.

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The movement of fluid up or down a narrow tube is capillarity. Capillary action, also known as capillarity, is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. This occurs because of the combination of two opposing forces: adhesion, the attraction between the liquid molecules and the inner surface of the tube, and cohesion, the attraction between the liquid molecules themselves. When the adhesion force is greater than the cohesion force, the liquid is pulled up the tube, and when the cohesion force is greater, the liquid is pushed down the tube. Capillarity is responsible for many natural phenomena, such as the ability of plants to transport water from their roots to their leaves, as well as some man-made ones, such as the operation of wicks in candles and the ink in fountain pens.

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In an R-C circuit, a resistor R and a capacitor C are connected in series to an AC voltage source. When an AC voltage is applied to a capacitor in a circuit, it takes some time to fully charge, as the capacitor acts like an open circuit to DC, but passes AC through it. As a result, the current flowing through the circuit will lag the voltage by some angle. This angle is determined by the ratio of the resistance and capacitance in the circuit. Therefore, in a R-C circuit, V^rms leads I^rms by 90^o.

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When the metal ball falls through the column of glycerine, it experiences both weight and upthrust, which opposes the motion of the ball. Eventually, the forces will be balanced and the velocity of the ball becomes constant, which is called terminal velocity. At this point, the forces on the ball are in equilibrium, which means that the weight of the ball (W) is equal to the upthrust (U) plus the viscous drag force (V). Therefore, the correct answer is: W = U + V Option (B)

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X-rays are produced when a metal target is used to block fast moving electrons. When high-speed electrons are fired at a metal target, they collide with the atoms in the target and produce X-rays. X-rays have short wavelengths and are highly penetrating, which makes them useful in medical imaging and materials analysis. Therefore, the correct statement among the options is "are produced when a metal target is used to block fast moving electrons."

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The period of a simple pendulum is the time it takes for one complete oscillation. In this case, we are given that the pendulum makes 50 oscillations in one minute. To find the period, we can use the formula: period = time / number of oscillations We know that the time for one minute is 60 seconds. So, we have: period = 60 seconds / 50 oscillations period = 1.2 seconds Therefore, the period of oscillation is 1.20 seconds, which corresponds to.

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The radiation emitted in radioactive decay that has momentum, a fairly high penetrating power, and is deflected by a magnet is the beta particle. Beta particles are fast-moving electrons or positrons emitted from the nucleus of an atom during radioactive decay. They have a negative charge, a mass of about 1/1836th of a proton, and can penetrate several millimeters of matter. Beta particles can be deflected by a magnetic field, which is a characteristic of charged particles in motion. In contrast, alpha particles are heavy particles consisting of two protons and two neutrons, which have a high ionizing power but are not deflected by a magnetic field. Gamma radiation and X-radiation are both electromagnetic radiation and do not have charge or mass, so they are not deflected by a magnetic field.

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Polarization is the property of waves that is exclusive to transverse waves. Polarization refers to the orientation of the oscillations of the wave, which can be either perpendicular or parallel to the direction of wave propagation. In a transverse wave, the oscillations are always perpendicular to the direction of propagation. This means that transverse waves can be polarized, while longitudinal waves cannot. Reflection, interference, and diffraction can occur in both transverse and longitudinal waves.

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The work function of a metal is the minimum amount of energy required to remove an electron from the surface of the metal. When the metal is irradiated with light of energy greater than the work function, electrons are emitted from the metal surface. The excess energy of the light is used to give kinetic energy to the ejected electron. In this case, the metal has a work function of 3.0eV and is irradiated with ultraviolet light of energy 4.0eV. Since the energy of the light is greater than the work function, electrons will be ejected from the metal surface. The kinetic energy of the ejected electron can be found by subtracting the work function from the energy of the incident light: Kinetic energy of ejected electron = Energy of incident light - Work function = 4.0eV - 3.0eV = 1.0eV Therefore, the kinetic energy of the ejected electron is 1.0eV.

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The SI unit of heat is the joule (J). Heat is a form of energy that is transferred from one body to another as a result of a difference in temperature. The amount of heat transferred is measured in joules, which is the amount of energy required to move an object with a force of one newton for a distance of one meter in the direction of the force. Therefore, the correct option is (a) joule. Kelvins (K) are used to measure temperature, watts (W) measure power and amperes (A) measure electric current.

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The average speed is defined as the total distance traveled divided by the total time taken. Let's first calculate the total distance traveled by the bird. Distance traveled in the first 3 seconds = speed × time = 10 ms\(^{-1}\) × 3 s = 30 m Distance traveled in the next 3 seconds = speed × time = 15 ms\(^{-1}\) × 3 s = 45 m Distance traveled in the next 4 seconds = speed × time = 20 ms\(^{-1}\) × 4 s = 80 m Total distance traveled = 30 m + 45 m + 80 m = 155 m Now let's calculate the total time taken: Total time taken = 3 s + 3 s + 4 s = 10 s Therefore, the average speed of the bird is: Average speed = Total distance traveled / Total time taken = 155 m / 10 s = 15.5 ms\(^{-1}\) So the correct option is: - 15.5 ms\(^{-1}\)

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The total capacitance of two capacitors connected in parallel is given by the sum of individual capacitances, which is 2μF + 2μF = 4μF. The charge on a capacitor is given by the product of its capacitance and the potential difference across it, which is Q = CV. Using the formula Q = CV and substituting the values, we get: Q = 4μF x 120V = 480μC Since there are two capacitors connected in parallel, the total charge is divided equally between them. Therefore, the charge on each capacitor is: Q/2 = 480μC/2 = 240μC So the answer is 2.4 x 10^-4C.

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The magnetic relay is a device used for controlling another circuit carrying a larger current. It consists of an electromagnet, a spring-loaded armature, and a set of contacts. When a current passes through the coil of the electromagnet, it generates a magnetic field which attracts the armature and causes it to move, closing or opening the contacts. This can be used to switch on or off a circuit carrying a larger current, or to switch between different circuits. The magnetic relay is commonly used in applications such as industrial automation, power systems, and telecommunications.

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A telescope is said to be in normal adjustment when the objective focal point coincides with that of the eyepiece. This means that the light rays coming in from the object being observed converge to a point at the same location where the eyepiece is positioned, allowing the viewer to see a magnified image. If the objective focal point is too far away from the eyepiece or if the focal lengths of the objective and eyepiece are not matched, the viewer will not be able to see a clear image. Therefore, adjusting the telescope to achieve normal adjustment is crucial for obtaining a clear, magnified image of the object being observed.

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When an object is dropped from rest, it falls under the influence of gravity. The distance it falls in time t is given by the formula: s = (1/2)gt² where g is the acceleration due to gravity. In this question, we are given t = 4s and g = 10 ms⁻². Substituting these values into the formula above, we get: s = (1/2) x 10 ms⁻² x (4 s)² = 80 m So, the height of the tower is 80 meters. Therefore, the correct answer is 80m.

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The time of flight is the total time taken by a projectile to complete its motion before it returns to the same level from which it was projected. The given expression for time of flight involves the initial velocity of the projectile (U), the angle of projection (theta) and the acceleration due to gravity (g). Therefore, the expression for the time of flight of a projectile is: \(\frac{2U sin \theta}{g}\) Option (C) matches the given expression and is the correct answer.

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Pressure is defined as force per unit area. Mathematically, pressure (P) can be expressed as P = F/A, where F is force and A is the area. The unit of force is newton (N) and the unit of area is square meter (m²). Therefore, the unit of pressure is N/m². This can be further simplified as kg m/s² / m² which gives kg m^-1s^-2. Therefore, option (B) is the correct answer.

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The most economical method of transmitting electrical power over long distances is alternating current at high voltage and low current. This is because the power loss in a transmission line is given by the formula P=I²R, where P is the power loss, I is the current and R is the resistance of the transmission line. By transmitting power at high voltage and low current, the current can be reduced, resulting in a lower power loss due to the lower value of I in the formula. This means that more power can be transmitted over longer distances with less loss, resulting in a more efficient and economical method of power transmission.

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A thermopile is a device that is used to detect radiant energy. When radiant energy is absorbed by a thermopile, it generates a small voltage, which can be measured by a voltmeter. This is because the thermopile is made up of a series of thermocouples, which are devices that generate a voltage when there is a difference in temperature between their ends. When the thermopile absorbs radiant energy, it causes a temperature difference between the ends of the thermocouples, which in turn generates a voltage. Therefore, the correct option is: radiant energy.

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The sound heard by a person after the reflection of the sound generated by him is called an "echo." An echo occurs when sound waves bounce off a hard surface and return to the listener's ear after a noticeable delay. The delay between the original sound and the reflected sound is called the "echo time." The quality of the echo is determined by the distance between the sound source and the reflecting surface, as well as the shape and size of the reflecting surface.

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The penetrating power of radiation is a measure of its ability to penetrate through matter. The more penetrating the radiation is, the farther it can travel through matter. In general, the penetrating power of radiation is inversely proportional to its ionizing power. - Alpha particles (\(\alpha\)): They are positively charged and have a large mass. They have a low penetrating power and are stopped by a sheet of paper or a few centimeters of air. - Beta particles (\(\beta\)): They are negatively charged and have a smaller mass compared to alpha particles. They have a higher penetrating power than alpha particles and can penetrate through a few millimeters of aluminum or several meters of air. - Gamma rays (\(\gamma\)): They are neutral and have no mass. They have the highest penetrating power and can penetrate through several centimeters of lead or many meters of concrete. Therefore, the correct order of decreasing penetrating power is \(\gamma, \beta, \alpha\). lists the radiations in this order.

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An atom in an excited state is one whose electrons have moved to higher energy levels. When an atom absorbs energy, its electrons move to higher energy levels, or orbitals, which are farther from the nucleus. When an electron moves from a lower energy level to a higher energy level, the atom is said to be in an excited state. Eventually, the electrons return to their original energy level by emitting energy in the form of electromagnetic radiation.

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The secondary colors of light are the colors that result from mixing two primary colors of light. The three primary colors of light are red, green, and blue. Option i consists of two primary colors of light (red and blue) and a secondary color of light (green). Therefore, it is not a set of secondary colors of light. Option ii consists of one primary color of light (blue) and two secondary colors of light (cyan and magenta). Therefore, it is a set of secondary colors of light. Option iii consists of two secondary colors of light (magenta and yellow) and a primary color of light (green). Therefore, it is not a set of secondary colors of light. Option iv consists of three secondary colors of light (cyan, magenta, and yellow). Therefore, it is a set of secondary colors of light. Thus, the correct answer is option ii and iv only.

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The given problem is related to optics and involves the use of the mirror formula. According to the mirror formula, 1/f = 1/v + 1/u where, f = focal length of the mirror u = object distance v = image distance The magnification produced by the mirror is given by the ratio of the height of the image to the height of the object. magnification = height of image / height of object From the problem statement, height of object (h) = 2.5 cm distance of object from the mirror (u) = 20 cm focal length of the mirror (f) = 10 cm Using the mirror formula, we can find the image distance (v) as: 1/10 = 1/v + 1/20 => 1/v = 1/10 - 1/20 => v = 20 cm The image is formed at a distance of 20 cm from the mirror. Now, using the magnification formula, we can find the height of the image as: magnification = height of image / height of object => height of image = magnification * height of object The magnification produced by a convex mirror is always less than 1. Therefore, the image formed will be smaller than the object. For a convex mirror, magnification = -v/u Substituting the given values, we get: magnification = -20/20 = -1 Therefore, the height of the image is given by: height of image = magnification * height of object => height of image = -1 * 2.5 cm => height of image = -2.5 cm Since the height of the image cannot be negative, we take its absolute value: height of image = |-2.5 cm| = 2.5 cm Hence, the height of the image is 2.5 cm. Therefore, the correct option is (a) 2.5 cm.

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As the temperature of the water in the syringe increases, the water molecules transfer some of their thermal energy to the trapped air molecules. This causes the air molecules to move faster, collide more frequently, and exert more pressure on the walls of the syringe. The increase in pressure of the trapped air forces the piston to move upwards, against the external atmospheric pressure. Therefore, the correct statement explaining the observation is "molecules of trapped air expands more".

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The core of a transformer is laminated in order to reduce eddy currents. Eddy currents are created by a magnetic field that is changing over time, inducing a current in the core. This current can cause energy loss and heating of the core, leading to inefficiencies in the transformer. Laminating the core creates many thin layers of material, each separated by a thin layer of insulation. This structure reduces the size of the current loops that can form and reduces the resistance of the current flow in the material. This reduction in eddy current also reduces energy loss, leading to greater efficiency of the transformer.

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The tendency for a stationary body to continue to remain at rest when a force is applied to it is known as inertia. Inertia is a fundamental property of matter that resists changes in motion, whether it is a stationary object or an object in motion. It is often described as the resistance of an object to changes in its state of motion, and it is directly related to an object's mass. The greater the mass of an object, the greater its inertia and the more force it will take to move it from a stationary position. This property of inertia is the reason why a heavy object requires more force to move than a light one.

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For a diverging lens, the image formed is always virtual, upright and smaller than the object. When the object is placed between the focal point and the optical center of the lens, the image formed will always be virtual, upright and will appear on the same side of the object. Also, the image will be formed by the diverging lens itself, so it will be between the lens and the focal point F on the same side as the object. Therefore, the correct option is (B) X and C.

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